Remote Sensing and Modelling of Inland Waters

*Inland Waters - Dynamics and Ecology*

2018;**114**:192-205. DOI: 10.1016/j.

Bharagava RN. Conventional methods for the removal of industrial pollutants, [49] Gekenidis MT, Qi W,

Hummerjohann J, Zbinden R, Walsh F, et al. Antibiotic-resistant indicator bacteria in irrigation water: High prevalence of extended-spectrum betalactamase (ESBL)-producing *Escherichia coli*. PLoS One. 2018;**13**(11):e0207857. DOI: 10.1371/journal.pone.0207857

[50] Jun C, Deng WJ, Liu YS, Hu LH, He LY, Zhao JL, et al. Fate and removal of antibiotics and antibiotic resistance genes in hybrid constructed wetlands. Environmental Pollution. 2019;**249**:894- 903. DOI: 10.1016/j.envpol.2019.03.111

[51] Czekalski N, Berthold T, Caucci S, Egli A, Bürgmann H. Increased levels of multiresistant bacteria and resistance genes after wastewater treatment and their dissemination into Lake Geneva, Switzerland. Frontiers in Microbiology.

[52] Adefisoye MA, Okoh AI. Id entification and antimicrobial resistance prevalence of pathogenic *Escherichia coli* strains from treated wastewater effluents in Eastern Cape, South Africa. Microbiology Open.

[53] Bai X, Ma X, Xu F, Li J, Zhang H, Xiao X. The drinking water treatment process as a potential source of affecting the bacterial antibiotic resistance. Science of the Total Environment.

[54] Fahrenfeld N, Ma Y, O'Brien M, Pruden A. Reclaimed water as a reservoir of antibiotic resistance genes: Distribution system and irrigation implications. Frontiers in Microbiology.

[55] Rizzo L, Manaia C, Merlin C, Schwartz T, Dagot C, Ploy M, et al. Urban wastewater treatment plants as hotspots for antibiotic resistant bacteria and genes spread into the environment:

A review. Science of the Total Environment. 2013, 447:345-360

2012, 2012;**3**:106

2016;**5**(1):143-151

2015;**533**:24-31

2013;**4**:130

[42] Mishra S, Chowdhary P,

their merits and demerits. In: Bharagava R, Chowdhary P, editors. Emerging and Eco-Friendly Approaches for Waste Management. Singapore:

[43] Chen H, Jing L, Yao Z, Meng F, Teng Y. Prevalence, source and risk of antibiotic resistance genes in the sediments of Lake Tai (China) deciphered by metagenomic assembly: A comparison with other global lakes. Environment International. 2019;**127**:267-275. DOI: 10.1016/j.

[44] Zhao W, Wang B, Yu G. Antibiotic resistance genes in China: Occurrence, risk, and correlation among different parameters. Environmental Science and Pollution Research. 2018, 2018;**25**(22):21467-21482

[45] Friedman ND, Temkin E, Carmeli Y. The negative impact of antibiotic resistance. Clinical Microbiology and Infection. 2016;**22**(5):416-422. DOI: 10.1016/j.

[46] Kümmerer K. Resistance in the environment. Journal of Antimicrobial Chemotherapy. 2004;**54**(2):311-320.

[47] Radhouani H, Silva N, Poeta P, Torres C, Correia S, Igrejas G. Potential impact of antimicrobial resistance in wildlife, environment and human health. Frontiers in Microbiology.

[48] Maryury BJ, Calero-Cáceres W, Muniesa M. Transfer of antibioticresistance genes via phage-related mobile elements. Plasmid. 2015;**79**:1-7. DOI: 10.1016/j.plasmid.2015.01.001

psep.2017.12.023

Springer; 2019

envint.2019.03.048

cmi.2015.12.002

DOI: 10.1093/jac/dkh325

2014;**5**:23. DOI: 10.3389/ fmicb.2014.00023.

**98**

**Chapter 7**

*Scott A. Wells*

**Abstract**

stratification

**101**

Modeling Thermal Stratification

Effects in Lakes and Reservoirs

A brief overview of characteristics of stratified water bodies is followed by an in-depth analysis of the governing equations for modeling hydrodynamics and water quality. Equations are presented for continuity or the fluid mass balance; x-momentum, y-momentum, and z-momentum equations; mass constituent balance equation; the heat balance equation for temperature; and the equation of state (relating density to temperature and concentration of dissolved and suspended solids). Additional equations and simplifications such as the water surface equation and changes to the pressure gradient term are shown. Many of the assumptions that are made in water quality models are discussed and shown. Typical water quality source-sink terms for temperature, dissolved oxygen, algae, and nutrients are listed. A summary of some typical water quality models for lakes and reservoirs is shown. Two case studies showing how models can predict temperature and dissolved oxygen dynamics in stratified reservoirs are shown. The brief summary looks at ways to

improve water quality and hydrodynamic models of lakes and reservoirs.

**Keywords:** water quality modeling, hydrodynamic modeling, temperature modeling, reservoir modeling, dissolved oxygen modeling, reservoir, lake,

Lakes and reservoirs are bodies of water that often serve multiple beneficial uses, such as water supply for municipal and agricultural use, recreation use, fishery enhancement, flood control, and power generation. Their physical, biological and chemical characteristics determine to a large extent how those beneficial uses are met. Survey texts, such as Wetzel [1] and Hutchinson [2], describe the important limnological processes that affect lake and reservoir water quality. An overview of reservoir dynamics and water quality is well-summarized in Martin et al. [3].

Lakes are different from man-made reservoirs where outlet (and perhaps inlet) hydraulic structures regulate the flow rates and often internal hydrodynamics of the reservoir. Not only does this flow regulation affect the reservoir temperature stratification, but also in consequence affects its water quality. An important distinction between rivers and lakes/reservoirs is the cycle of stratification that can occur

In some river systems though, stratification can occur if there are natural pools. For example, in the Chehalis River basin in Washington, USA, the Chehalis River is usually well-mixed except in pools of slow-moving water. This is shown where a

throughout the year since most rivers are well-mixed vertically.

**1. Characteristics of lakes and reservoirs**

#### **Chapter 7**

### Modeling Thermal Stratification Effects in Lakes and Reservoirs

*Scott A. Wells*

#### **Abstract**

A brief overview of characteristics of stratified water bodies is followed by an in-depth analysis of the governing equations for modeling hydrodynamics and water quality. Equations are presented for continuity or the fluid mass balance; x-momentum, y-momentum, and z-momentum equations; mass constituent balance equation; the heat balance equation for temperature; and the equation of state (relating density to temperature and concentration of dissolved and suspended solids). Additional equations and simplifications such as the water surface equation and changes to the pressure gradient term are shown. Many of the assumptions that are made in water quality models are discussed and shown. Typical water quality source-sink terms for temperature, dissolved oxygen, algae, and nutrients are listed. A summary of some typical water quality models for lakes and reservoirs is shown. Two case studies showing how models can predict temperature and dissolved oxygen dynamics in stratified reservoirs are shown. The brief summary looks at ways to improve water quality and hydrodynamic models of lakes and reservoirs.

**Keywords:** water quality modeling, hydrodynamic modeling, temperature modeling, reservoir modeling, dissolved oxygen modeling, reservoir, lake, stratification

#### **1. Characteristics of lakes and reservoirs**

Lakes and reservoirs are bodies of water that often serve multiple beneficial uses, such as water supply for municipal and agricultural use, recreation use, fishery enhancement, flood control, and power generation. Their physical, biological and chemical characteristics determine to a large extent how those beneficial uses are met. Survey texts, such as Wetzel [1] and Hutchinson [2], describe the important limnological processes that affect lake and reservoir water quality. An overview of reservoir dynamics and water quality is well-summarized in Martin et al. [3].

Lakes are different from man-made reservoirs where outlet (and perhaps inlet) hydraulic structures regulate the flow rates and often internal hydrodynamics of the reservoir. Not only does this flow regulation affect the reservoir temperature stratification, but also in consequence affects its water quality. An important distinction between rivers and lakes/reservoirs is the cycle of stratification that can occur throughout the year since most rivers are well-mixed vertically.

In some river systems though, stratification can occur if there are natural pools. For example, in the Chehalis River basin in Washington, USA, the Chehalis River is usually well-mixed except in pools of slow-moving water. This is shown where a

large area of the Chehalis river has little to no channel slope and exhibits lake-like characteristics in **Figure 1**.

Stratification in turn is related to the density of water as a function of temperature and dissolved substances. The progression of stratification during a summer period is shown in **Figure 2** in a mountain lake during a summer period where the upper well-mixed layer, the epilimnion, is separated from the lower layer, the hypolimnion, by the strong density (temperature) gradient. **Figure 3** shows the typical inverse stratification in the wintertime. Oftentimes, ice formation on the surface can impede gas transfer and create winter-time oxygen deficits even though there is reduced biological activity as a result of the cold temperatures.

The progression of summer stratification can also influence the progression of dissolved oxygen depletion (see **Figure 4** for Tenkiller Reservoir, OK, USA). This

**Figure 1.**

*Elevation drop along the Chehalis River, WA, USA, showing a section that is lake-like where summer stratification occurs. Sampling sites (multi-colored dots) are also shown.*

seasonal depletion in **Figure 4** includes both the metalimnetic minimum (caused by hydrodynamic interflow of low-dissolved oxygen water at the base of the epilimnion) and the hypolimnetic depletion as a result of sediment oxygen demand.

*Tenkiller reservoir dissolved oxygen profiles in 2006 showing progression of summer oxygen depletion.*

**Figure 3.**

**Figure 4.**

**103**

*Bull Run Lake, OR, USA, temperature profile on January 19, 1993.*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

Also, as a result of internal seiching, wind dynamics, surface cooling, and solar radiation input, the vertical profiles for water quality parameters can vary during the day. For example, Hemlock Lake temperature and dissolved oxygen vertical profiles are shown in **Figures 5** and **6**, respectively, for the morning (9 am) and early afternoon (1 pm). Variation of 1–2°C and 4–5 mg/l dissolved oxygen concentrations were noted over the 4-hour time difference between profiles. Showing the effect of diurnal wind on seiching dynamics, **Figure 7** shows a temperature buoy at a depth of 15 m in Chester Morse Lake, WA, USA, where variations of 2–3°C can be common diurnally as wind-induced seiching occurs.

In order to describe these changes in water quality in a lake or reservoir, the next section describes the mathematical framework for modeling lakes and reservoirs.

**Figure 2.** *Progression of stratification in summer of Bull Run Lake, OR, USA, during 1997.*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

large area of the Chehalis river has little to no channel slope and exhibits lake-like

there is reduced biological activity as a result of the cold temperatures.

*Elevation drop along the Chehalis River, WA, USA, showing a section that is lake-like where summer*

*stratification occurs. Sampling sites (multi-colored dots) are also shown.*

*Progression of stratification in summer of Bull Run Lake, OR, USA, during 1997.*

Stratification in turn is related to the density of water as a function of temperature and dissolved substances. The progression of stratification during a summer period is shown in **Figure 2** in a mountain lake during a summer period where the upper well-mixed layer, the epilimnion, is separated from the lower layer, the hypolimnion, by the strong density (temperature) gradient. **Figure 3** shows the typical inverse stratification in the wintertime. Oftentimes, ice formation on the surface can impede gas transfer and create winter-time oxygen deficits even though

The progression of summer stratification can also influence the progression of dissolved oxygen depletion (see **Figure 4** for Tenkiller Reservoir, OK, USA). This

characteristics in **Figure 1**.

*Inland Waters - Dynamics and Ecology*

**Figure 1.**

**Figure 2.**

**102**

**Figure 3.** *Bull Run Lake, OR, USA, temperature profile on January 19, 1993.*

**Figure 4.** *Tenkiller reservoir dissolved oxygen profiles in 2006 showing progression of summer oxygen depletion.*

seasonal depletion in **Figure 4** includes both the metalimnetic minimum (caused by hydrodynamic interflow of low-dissolved oxygen water at the base of the epilimnion) and the hypolimnetic depletion as a result of sediment oxygen demand.

Also, as a result of internal seiching, wind dynamics, surface cooling, and solar radiation input, the vertical profiles for water quality parameters can vary during the day. For example, Hemlock Lake temperature and dissolved oxygen vertical profiles are shown in **Figures 5** and **6**, respectively, for the morning (9 am) and early afternoon (1 pm). Variation of 1–2°C and 4–5 mg/l dissolved oxygen concentrations were noted over the 4-hour time difference between profiles.

Showing the effect of diurnal wind on seiching dynamics, **Figure 7** shows a temperature buoy at a depth of 15 m in Chester Morse Lake, WA, USA, where variations of 2–3°C can be common diurnally as wind-induced seiching occurs.

In order to describe these changes in water quality in a lake or reservoir, the next section describes the mathematical framework for modeling lakes and reservoirs.

**Figure 5.** *Hemlock Lake, NY, USA temperature profile July 13, 2013 at 9 am and 1 pm.*

momentum is based on evaluating the sum of forces acting on a control volume in *x*, *y*, or *z* (for a Cartesian system) and equating these to the acceleration of a control volume as shown in **Figure 8**. Mathematically, conservation of momentum is

*Example of a force acting on a control volume resulting in the acceleration of the fluid within the control*

*Internal seiching as evident in temperature dynamics at a depth of 15 m in Chester Morse Lake, WA, USA. Variations of 2°C occur at a diurnal time scale are evident during the later spring and summer as a result of*

!: acceleration of fluid within control volume.

!: vector forces acting on control volume, m: mass

described as P *F*

**Figure 7.**

**Figure 8.**

*volume.* **105**

within control volume, *a*

!

<sup>¼</sup> *ma*!, where *<sup>F</sup>*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

*wind seiching and closeness to vertical temperature gradient.*

**Figure 6.**

*Hemlock Lake, NY, USA dissolved oxygen profile July 13, 2013 at 9 am and 1 pm.*

#### **2. Governing equations for lake and reservoir water quality modeling**

The basic governing equations for hydrodynamics and water quality were discussed by Wells et al. [4] and summarized and simplified here. The hydrodynamic governing equations include conservation of water mass and momentum. The water quality governing equations include conservation of constituent mass and heat including processes such as advection, turbulent diffusion, molecular diffusion (and dispersion if there is spatial averaging). An equation of state is used to relate the water density to salinity, temperature, and suspended solids that can affect fluid momentum.

#### **2.1 Governing equations for mass, momentum, constituent mass and heat conservation**

The equations for fluid motion are based on mass and momentum conservation. The development of the governing equations is based on a control volume of homogeneous properties. The conservation of fluid mass is the change in fluid mass within the control volume equaling the sum of mass inflows to the control volume and the sum of mass outflows from the control volume. The conservation of

#### *Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

#### **Figure 7.**

*Internal seiching as evident in temperature dynamics at a depth of 15 m in Chester Morse Lake, WA, USA. Variations of 2°C occur at a diurnal time scale are evident during the later spring and summer as a result of wind seiching and closeness to vertical temperature gradient.*

momentum is based on evaluating the sum of forces acting on a control volume in *x*, *y*, or *z* (for a Cartesian system) and equating these to the acceleration of a control volume as shown in **Figure 8**. Mathematically, conservation of momentum is described as P *F* ! <sup>¼</sup> *ma*!, where *<sup>F</sup>* !: vector forces acting on control volume, m: mass within control volume, *a* !: acceleration of fluid within control volume.

**2. Governing equations for lake and reservoir water quality modeling**

*Hemlock Lake, NY, USA dissolved oxygen profile July 13, 2013 at 9 am and 1 pm.*

*Hemlock Lake, NY, USA temperature profile July 13, 2013 at 9 am and 1 pm.*

**2.1 Governing equations for mass, momentum, constituent mass and heat**

The development of the governing equations is based on a control volume of homogeneous properties. The conservation of fluid mass is the change in fluid mass within the control volume equaling the sum of mass inflows to the control volume and the sum of mass outflows from the control volume. The conservation of

The equations for fluid motion are based on mass and momentum conservation.

**conservation**

**104**

**Figure 5.**

*Inland Waters - Dynamics and Ecology*

**Figure 6.**

The basic governing equations for hydrodynamics and water quality were discussed by Wells et al. [4] and summarized and simplified here. The hydrodynamic governing equations include conservation of water mass and momentum. The water quality governing equations include conservation of constituent mass and heat including processes such as advection, turbulent diffusion, molecular diffusion (and dispersion if there is spatial averaging). An equation of state is used to relate the water density to salinity, temperature, and suspended solids that can affect fluid momentum.

The general coordinate system used in the development of the governing equations is shown in **Figure 9**. The rotation of the coordinate system can result in significant horizontal accelerations of fluids. This is usually restricted to large water bodies such as large lakes (such as the Great Lakes in the USA) and oceanic systems. The body force that causes horizontal accelerations because of the spinning coordinate system is termed the Coriolis force.

*2.1.1 Continuity*

that *<sup>∂</sup><sup>η</sup> <sup>∂</sup><sup>t</sup>* <sup>¼</sup> *<sup>∂</sup> ∂x* Ð *h <sup>η</sup> udz* <sup>þ</sup> *<sup>∂</sup> ∂y* Ð *h <sup>η</sup> vdz* � <sup>Ð</sup> *<sup>h</sup>*

*2.1.2 X-momentum equation*

*∂u ∂t* |{z} unsteady acceleration

> ¼ � <sup>1</sup> *ρ ∂p ∂x* |{z} pressure gradient

where: *τxx* ¼ *ρu*<sup>0</sup>

ized as *<sup>τ</sup>xx* <sup>¼</sup> *<sup>μ</sup>turbulent*�*xx <sup>∂</sup><sup>u</sup>*

becomes after simplification � <sup>1</sup>

*2.1.3 Y-momentum equation*

*∂v ∂t* þ *u ∂v ∂x* þ *v ∂v ∂y* þ *w ∂v ∂z*

where: *τyx* ¼ *ρv*<sup>0</sup>

the x-face of control volume, *τyy* ¼ *ρv*<sup>0</sup>

*ρu*<sup>0</sup>

**107**

*pa* þ *g* Ð *z* þ *u ∂u ∂x* þ *v ∂u ∂y* þ *w ∂u ∂z*

the x-face of control volume, *τxy* ¼ *ρu*<sup>0</sup>

þ *μ ρ*

*∂u ∂x* þ *∂v ∂y* þ *∂w*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

cell in units of flow rate per unit length, z = h is the location of the bottom referenced to a datum, and z=η is the water surface level referenced to a datum.

This equation is used to solve for the water surface elevation.


> *∂*2 *u ∂x*<sup>2</sup> þ

acting in x direction on the y-face of control volume, *τxz* ¼ *ρu*<sup>0</sup>

*<sup>∂</sup><sup>x</sup>* ¼ *ρu*<sup>0</sup>

*u*0

*ρ ∂p <sup>∂</sup><sup>x</sup>* ¼ � <sup>1</sup> *ρ ∂pa <sup>∂</sup><sup>x</sup>* <sup>þ</sup> *<sup>g</sup> <sup>∂</sup><sup>η</sup>*

acting in y direction on the y-face of control volume, *τyz* ¼ *ρv*<sup>0</sup>

*∂*2 *u ∂y*<sup>2</sup> þ


turbulent shear stress acting in x direction on the z-face of control volume,

viscosity. The pressure is usually decomposed into the following terms: *p* ¼

acceleration due to gravity. The pressure gradient in the x-momentum then

<sup>þ</sup> <sup>2</sup>*Ωzu* ¼ � <sup>1</sup>

μ = dynamic viscosity, Ω = component of Coriolis acceleration where: *Ω<sup>z</sup>* ¼ *Ω<sup>E</sup> sin φ*, *Ω<sup>y</sup>* ¼ *Ω<sup>E</sup> cos φ*, ϕ ¼ latitude, *Ω<sup>E</sup>* ¼ earth'*s* rotation rate, and assuming 2*Ωyw* is negligible. In general, the molecular viscous stresses are negligible except at boundaries. Analogous to laminar shear stress, the turbulent shear stresses are often parameter-

, *τxx* ¼ *μturbulent*�*xy*

*w*<sup>0</sup> where the term *μturbulent* is the turbulent eddy viscosity analogous to molecular

*<sup>η</sup> ρdz* where pa is the atmospheric pressure on the water surface and g is the

*ρ ∂p ∂y* þ *μ ρ*

þ 1 *ρ* *<sup>∂</sup><sup>x</sup>* � *<sup>g</sup> ρ* Ð *z η ∂ρ <sup>∂</sup><sup>x</sup> dz*.

*∂τyx ∂x* þ *∂τyy ∂y* þ *∂τyz ∂z* � � (3)

*u*<sup>0</sup> where τyx is the turbulent shear stress acting in y direction on

*∂*2 *v ∂x*<sup>2</sup> þ *∂*2 *v ∂y*<sup>2</sup> þ

*v*<sup>0</sup> where τyy is the turbulent shear stress

� �

*∂*2 *v ∂z*<sup>2</sup>

*w*<sup>0</sup> where τyz is the

� �

where *u*: temporal mean velocity in the x-direction, *v*: temporal mean velocity in the y-direction, *w*: temporal mean velocity in the z-direction. The continuity equation is usually also integrated vertically to provide the water surface equation, such

> � 2*Ωzv* |ffl{zffl} Coriolis acceleration

> > þ 1 *ρ*

*∂τxx ∂x* þ *∂τxy ∂y* þ *∂τxz ∂z*

*u*<sup>0</sup> where τxx is the turbulent shear stress acting in x direction on

*∂u <sup>∂</sup><sup>y</sup>* ¼ *ρu*<sup>0</sup> *v*0

� �

(2)

*<sup>∂</sup><sup>z</sup>* ¼


*v*<sup>0</sup> where τxy is the turbulent shear stress

*w*0

where τxz is the

, *<sup>τ</sup>xz* <sup>¼</sup> *<sup>μ</sup>turbulent*�*xz <sup>∂</sup><sup>u</sup>*

*∂*2 *u ∂z*<sup>2</sup>

*<sup>∂</sup><sup>z</sup>* <sup>¼</sup> <sup>0</sup> (1)

*<sup>η</sup> qdz* where q is removal from or inflow to a model

The continuity (or conservation of fluid mass) and the conservation of momentum equations for a rotating coordinate system [5–7] are the governing equations used to determine the velocity field and water level.

The final form of the governing equations is obtained by making the following assumptions:


The governing equations become after time averaging and simplifying:

#### **Figure 9.**

*Definition sketch of coordinate system for governing equations where x is oriented east, y is oriented north, and z is oriented upward opposite gravity, Ω is the angular velocity of the earth spinning on its axis and ϕ is the latitude.*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

#### *2.1.1 Continuity*

The general coordinate system used in the development of the governing equa-

The continuity (or conservation of fluid mass) and the conservation of momentum equations for a rotating coordinate system [5–7] are the governing equations

The final form of the governing equations is obtained by making the following

• the centripetal acceleration is a correction to gravitational acceleration,

• the Boussinesq approximation (which is related to the incompressibility assumption) is applied to all terms in the momentum equation except those

• all velocities and pressure are turbulent time averages, i.e., *u* ¼ *u* þ *u*´, where

The governing equations become after time averaging and simplifying:

*Definition sketch of coordinate system for governing equations where x is oriented east, y is oriented north, and z is oriented upward opposite gravity, Ω is the angular velocity of the earth spinning on its axis and ϕ is the*

*<sup>t</sup> udt* and ´*u* is the temporal fluctuation of u about the mean, and similarly for the velocity in the y-direction, *v* ¼ *v* þ *v*´, the velocity in the z

dealing with density gradient induced accelerations, i.e. <sup>1</sup>

direction *w* ¼ *w* þ *w*´ , and the pressure, *p* ¼ *p* þ *p*´

*<sup>ρ</sup>* < <1 where ρ is the fluid density and Δρ

*<sup>ρ</sup>* <sup>¼</sup> <sup>1</sup> *<sup>ρ</sup>o*þ*Δρ*<sup>≈</sup> <sup>1</sup> *ρo* where

tions is shown in **Figure 9**. The rotation of the coordinate system can result in significant horizontal accelerations of fluids. This is usually restricted to large water bodies such as large lakes (such as the Great Lakes in the USA) and oceanic systems. The body force that causes horizontal accelerations because of the spinning coordi-

nate system is termed the Coriolis force.

*Inland Waters - Dynamics and Ecology*

• the fluid is incompressible, where *Δρ*

*ρ* ¼ *ρ<sup>o</sup>* þ *Δρ*, *ρ<sup>o</sup>* is a base value,

is the change in density,

assumptions:

*<sup>u</sup>* <sup>¼</sup> <sup>1</sup> *T* Ð*<sup>t</sup>*þ*<sup>T</sup>*

**Figure 9.**

*latitude.*

**106**

used to determine the velocity field and water level.

$$\frac{\partial \overline{u}}{\partial \mathbf{x}} + \frac{\partial \overline{v}}{\partial \mathbf{y}} + \frac{\partial \overline{w}}{\partial \mathbf{z}} = \mathbf{0} \tag{1}$$

where *u*: temporal mean velocity in the x-direction, *v*: temporal mean velocity in the y-direction, *w*: temporal mean velocity in the z-direction. The continuity equation is usually also integrated vertically to provide the water surface equation, such that *<sup>∂</sup><sup>η</sup> <sup>∂</sup><sup>t</sup>* <sup>¼</sup> *<sup>∂</sup> ∂x* Ð *h <sup>η</sup> udz* <sup>þ</sup> *<sup>∂</sup> ∂y* Ð *h <sup>η</sup> vdz* � <sup>Ð</sup> *<sup>h</sup> <sup>η</sup> qdz* where q is removal from or inflow to a model cell in units of flow rate per unit length, z = h is the location of the bottom referenced to a datum, and z=η is the water surface level referenced to a datum. This equation is used to solve for the water surface elevation.

#### *2.1.2 X-momentum equation*

where: *τxx* ¼ *ρu*<sup>0</sup> *u*<sup>0</sup> where τxx is the turbulent shear stress acting in x direction on the x-face of control volume, *τxy* ¼ *ρu*<sup>0</sup> *v*<sup>0</sup> where τxy is the turbulent shear stress acting in x direction on the y-face of control volume, *τxz* ¼ *ρu*<sup>0</sup> *w*0 where τxz is the turbulent shear stress acting in x direction on the z-face of control volume, μ = dynamic viscosity, Ω = component of Coriolis acceleration where: *Ω<sup>z</sup>* ¼ *Ω<sup>E</sup> sin φ*, *Ω<sup>y</sup>* ¼ *Ω<sup>E</sup> cos φ*, ϕ ¼ latitude, *Ω<sup>E</sup>* ¼ earth'*s* rotation rate, and assuming 2*Ωyw* is negligible. In general, the molecular viscous stresses are negligible except at boundaries. Analogous to laminar shear stress, the turbulent shear stresses are often parameterized as *<sup>τ</sup>xx* <sup>¼</sup> *<sup>μ</sup>turbulent*�*xx <sup>∂</sup><sup>u</sup> <sup>∂</sup><sup>x</sup>* ¼ *ρu*<sup>0</sup> *u*0 , *τxx* ¼ *μturbulent*�*xy ∂u <sup>∂</sup><sup>y</sup>* ¼ *ρu*<sup>0</sup> *v*0 , *<sup>τ</sup>xz* <sup>¼</sup> *<sup>μ</sup>turbulent*�*xz <sup>∂</sup><sup>u</sup> <sup>∂</sup><sup>z</sup>* ¼ *ρu*<sup>0</sup> *w*<sup>0</sup> where the term *μturbulent* is the turbulent eddy viscosity analogous to molecular viscosity. The pressure is usually decomposed into the following terms: *p* ¼ *pa* þ *g* Ð *z <sup>η</sup> ρdz* where pa is the atmospheric pressure on the water surface and g is the acceleration due to gravity. The pressure gradient in the x-momentum then becomes after simplification � <sup>1</sup> *ρ ∂p <sup>∂</sup><sup>x</sup>* ¼ � <sup>1</sup> *ρ ∂pa <sup>∂</sup><sup>x</sup>* <sup>þ</sup> *<sup>g</sup> <sup>∂</sup><sup>η</sup> <sup>∂</sup><sup>x</sup>* � *<sup>g</sup> ρ* Ð *z η ∂ρ <sup>∂</sup><sup>x</sup> dz*.

#### *2.1.3 Y-momentum equation*

$$\begin{array}{c} \frac{\partial \overline{\boldsymbol{w}}}{\partial t} + \overline{\boldsymbol{u}} \frac{\partial \overline{\boldsymbol{v}}}{\partial \boldsymbol{x}} + \overline{\boldsymbol{v}} \frac{\partial \overline{\boldsymbol{w}}}{\partial \boldsymbol{y}} + \overline{\boldsymbol{w}} \frac{\partial \overline{\boldsymbol{w}}}{\partial \boldsymbol{x}} + 2\boldsymbol{\Omega}\_{\overline{\boldsymbol{x}}} \overline{\boldsymbol{u}} = -\frac{1}{\rho} \frac{\partial \overline{\boldsymbol{p}}}{\partial \boldsymbol{y}} + \frac{\mu}{\rho} \left( \frac{\partial^{2} \overline{\boldsymbol{v}}}{\partial \boldsymbol{x}^{2}} + \frac{\partial^{2} \overline{\boldsymbol{v}}}{\partial \boldsymbol{y}^{2}} + \frac{\partial^{2} \overline{\boldsymbol{v}}}{\partial \boldsymbol{z}^{2}} \right) \\ & + \frac{1}{\rho} \left( \frac{\partial \mathsf{r}\_{\rm{yx}}}{\partial \boldsymbol{x}} + \frac{\partial \mathsf{r}\_{\rm{yy}}}{\partial \boldsymbol{y}} + \frac{\partial \mathsf{r}\_{\rm{yx}}}{\partial \boldsymbol{z}} \right) \end{array} \tag{3}$$

where: *τyx* ¼ *ρv*<sup>0</sup> *u*<sup>0</sup> where τyx is the turbulent shear stress acting in y direction on the x-face of control volume, *τyy* ¼ *ρv*<sup>0</sup> *v*<sup>0</sup> where τyy is the turbulent shear stress acting in y direction on the y-face of control volume, *τyz* ¼ *ρv*<sup>0</sup> *w*<sup>0</sup> where τyz is the

turbulent shear stress acting in y direction on the z-face of control volume, and assuming �2*Ωxw* is negligible. Analogous to laminar shear stress, the turbulent shear stresses are often parameterized as *τyx* ¼ *μturbulent*�*yx ∂v <sup>∂</sup><sup>x</sup>* ¼ *ρv*<sup>0</sup> *u*0 , *τyy* ¼ *μturbulent*�*yy ∂v <sup>∂</sup><sup>y</sup>* ¼ *ρv*<sup>0</sup> *v*0 , *<sup>τ</sup>yz* <sup>¼</sup> *<sup>μ</sup>turbulent*�*xz <sup>∂</sup><sup>v</sup> <sup>∂</sup><sup>z</sup>* ¼ *ρv*<sup>0</sup> *w*0 . The pressure is usually decomposed into the following terms: *p* ¼ *pa* þ *g* Ð *z <sup>η</sup> ρdz*, and the pressure gradient in the y-momentum then becomes after simplification � <sup>1</sup> *ρ ∂p <sup>∂</sup><sup>y</sup>* ¼ � <sup>1</sup> *ρ ∂pa <sup>∂</sup><sup>y</sup>* <sup>þ</sup> *<sup>g</sup> <sup>∂</sup><sup>η</sup> <sup>∂</sup><sup>y</sup>* � *<sup>g</sup> ρ* Ð *z η ∂ρ <sup>∂</sup><sup>y</sup> dz*.

Substituting the time average and fluctuating components of concentration and

� � � �


where the turbulent mass fluxes in x, y and z were assumed to be defined as a

/T], Ez is the turbulent mass diffusivity in z [L<sup>2</sup>

terms in the governing equation represent mass transport by turbulent eddies. As

In turbulent fluids, Ex, Ey, and Ez >> D, and D can be neglected (except at boundaries or density interfaces where turbulent intensity may approach zero). The turbulent diffusion coefficients can be thought of as the product of the velocity scale of turbulence and the length scale of that turbulence. These coefficients are related to the turbulent eddy viscosity. In general, these turbulent diffusion coeffi-

Spatial averaging of this equation leads to the introduction of "dispersion" coefficients which account for the transport of mass as a result of spatial irregularities in

These equations are also valid for heat transport and temperature modeling by

¼ *DT*

� � � �


where DT is the molecular thermal conductivity for heat and Ex, Ey, and Ez are the heat and mass turbulent eddy diffusivities assuming they are of the same order

Since density is an important variable for the momentum equation to account for density-driven flows, the computation of density is accomplished through an equation of state where density is computed from dissolved and suspended solids

concentrations (*cdissolved solids*,*csuspended solids*Þ and temperature, T, such as

*∂*2 *T ∂x*<sup>2</sup> � �

> þ *∂ ∂z Ez ∂T ∂z*

þ

*∂*2 *T ∂y*<sup>2</sup> � �


� � � �

þ

þ

*∂*2 *T ∂z*<sup>2</sup>

*S ρcp* |{z} heat flux (7)

substituting the concentration of heat, *ρcpT*, where T is temperature, cp is the coefficient of specific heat at constant pressure and ρ is the density, such that the

> þ *∂ ∂y Ey ∂T ∂y* � �

governing equation for temperature, T, becomes after simplification


the intensity of turbulence increases, turbulent mass transport increases.

<sup>¼</sup> *<sup>D</sup> <sup>∂</sup>*<sup>2</sup>

þ *∂ ∂z Ez ∂c ∂z*

� � ¼ �*Ex <sup>∂</sup><sup>c</sup>*

*c ∂x*<sup>2</sup> � �

þ

*<sup>∂</sup>x*, *v*´´*c*

� � ¼ �*Ey*

/T], Ey is the turbulent mass

*∂*2 *c ∂y*<sup>2</sup> � �


� � � �

þ

þ *S* |{z} sources*=*sinks

> *∂c ∂y* , *w*´ ´*c* � � <sup>¼</sup>

/T]. The new

*∂*2 *c ∂z*<sup>2</sup>

(6)

velocities into the 3D governing equation and time averaging we obtain:

þ *∂ ∂y Ey ∂c ∂y* � �


*∂c ∂t* |{z} unsteady change in concentration

�*Ez <sup>∂</sup><sup>c</sup> ∂z*

diffusivity in y[L2

the velocity field.

*∂T ∂t* |{z} unsteady change in temperature

of magnitude.

**109**

**2.3 Equation of state**

þ *u*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

þ *∂ ∂x Ex ∂c ∂x* � �

gradient, diffusion-type process, such as *u*´´*c*

cients are non-isotropic and non-homogeneous.

þ *u*

*∂T ∂x* þ *v ∂T ∂y* þ *w ∂T ∂z*

þ *∂ ∂x Ex ∂T ∂x* � �

, Ex is the turbulent mass diffusivity in x [L<sup>2</sup>

*∂c ∂x* þ *v ∂c ∂y* þ *w ∂c ∂z*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

#### *2.1.4 Z-momentum equation*

$$\begin{aligned} \frac{\partial \overline{w}}{\partial t} + \overline{u} \frac{\partial \overline{w}}{\partial \mathbf{x}} + \overline{v} \frac{\partial \overline{w}}{\partial \mathbf{y}} + \overline{w} \frac{\partial \overline{w}}{\partial \mathbf{z}} &= -\mathbf{g} - \frac{\mathbf{1}}{\rho} \frac{\partial \overline{p}}{\partial \mathbf{z}} + \frac{\mu}{\rho} \left( \frac{\partial^2 \overline{w}}{\partial \mathbf{x}^2} + \frac{\partial^2 \overline{w}}{\partial \mathbf{y}^2} + \frac{\partial^2 \overline{w}}{\partial \mathbf{z}^2} \right) \\ &+ \frac{\mathbf{1}}{\rho} \left( \frac{\partial \mathbf{r\_{xx}}}{\partial \mathbf{x}} + \frac{\partial \mathbf{r\_{xy}}}{\partial \mathbf{y}} + \frac{\partial \mathbf{r\_{xz}}}{\partial \mathbf{z}} \right) \end{aligned} \tag{4}$$

where: *τzx* ¼ *ρw*<sup>0</sup> *u*<sup>0</sup> where τzx is the turbulent shear stress acting in z direction on the x-face of control volume, *τzy* ¼ *ρw*<sup>0</sup> *v*<sup>0</sup> where τzy is the turbulent shear stress acting in z direction on the y-face of control volume, *τzz* ¼ *ρw*<sup>0</sup> *w*<sup>0</sup> where τzz is the turbulent shear stress acting in z direction on the z-face of control volume, and neglecting the Coriolis terms �2*Ωyu* þ 2*Ωxv*. Analogous to laminar shear stress, the turbulent shear stresses are often parameterized as *<sup>τ</sup>zx* <sup>¼</sup> *<sup>μ</sup>turbulent*�*zx <sup>∂</sup><sup>w</sup> <sup>∂</sup><sup>x</sup>* ¼ *ρw*<sup>0</sup> *u*0 , *τzy* ¼ *μturbulent*�*zy ∂w <sup>∂</sup><sup>y</sup>* ¼ *ρw*<sup>0</sup> *v*0 , *<sup>τ</sup>zz* <sup>¼</sup> *<sup>μ</sup>turbulent*�*zz <sup>∂</sup><sup>w</sup> <sup>∂</sup><sup>z</sup>* ¼ *ρw*<sup>0</sup> *w*0 . In cases where vertical accelerations are much less than horizontal accelerations, this equation can be reduced to the hydrostatic equation, i.e., <sup>1</sup> *ρ ∂p <sup>∂</sup><sup>z</sup>* ¼ �*g*.

#### **2.2 Conservation of constituent mass and heat: the ADVECTIVE diffusion equation**

The conservation of constituent mass in a control volume is a sum of all the fluxes (advective and diffusive) into and out from the control volume plus sources and sinks (chemistry, biology, physics, withdrawals, inputs) within the control volume. Summing up the fluxes in each direction, assuming that the fluid is incompressible and that the molecular diffusivity, D, is homogeneous and isotropic, the advective diffusion equation becomes

$$\underbrace{\frac{\partial c}{\partial t}}\_{\text{unstable}} + \underbrace{u \frac{\partial c}{\partial x} + v \frac{\partial c}{\partial y} + w \frac{\partial c}{\partial z}}\_{\text{advective mass transport}} = \underbrace{D \left[ \left( \frac{\partial^2 c}{\partial x^2} \right) + \left( \frac{\partial^2 c}{\partial y^2} \right) + \left( \frac{\partial^2 c}{\partial z^2} \right) \right]}\_{\text{diffusive mass transport}} + \underbrace{\mathcal{S}}\_{\text{source/sink}} \tag{5}$$

where c is the concentration [M/L�<sup>3</sup> ], S is the sources and sinks of reactions occurring in the control volume, or the reaction rate [ML�<sup>3</sup> T�<sup>1</sup> ].

This equation is a 3-D, unsteady equation that applies to all flow conditions: laminar and turbulent. Since we cannot determine the instantaneous velocity field, the x-y-and z momentum equations were time averaged and hence were only able to practically predict the temporal mean velocity. Similarly, we time average the conservation of mass/heat equation using time averages of the velocity field.

The instantaneous velocity and concentration are decomposed into a mean and an unsteady component. Similar to the velocity field shown earlier, for concentration, c, this becomes *<sup>c</sup>* <sup>¼</sup> *<sup>c</sup>* <sup>þ</sup> *<sup>c</sup>*<sup>0</sup> where *<sup>c</sup>* <sup>¼</sup> <sup>1</sup> *T* Ð*<sup>t</sup>*þ*<sup>T</sup> <sup>t</sup> cdt* and *c*<sup>0</sup> is the fluctuation about the mean.

turbulent shear stress acting in y direction on the z-face of control volume, and assuming �2*Ωxw* is negligible. Analogous to laminar shear stress, the turbulent

*<sup>∂</sup><sup>z</sup>* ¼ *ρv*<sup>0</sup>

*ρ ∂p ∂z* þ *μ ρ*

*∂τzx ∂x* þ *∂τzy ∂y* þ *∂τzz ∂z*

*<sup>∂</sup><sup>z</sup>* ¼ �*<sup>g</sup>* � <sup>1</sup>

þ 1 *ρ*

turbulent shear stress acting in z direction on the z-face of control volume, and neglecting the Coriolis terms �2*Ωyu* þ 2*Ωxv*. Analogous to laminar shear stress, the

accelerations are much less than horizontal accelerations, this equation can be

**2.2 Conservation of constituent mass and heat: the ADVECTIVE diffusion**

<sup>¼</sup> *<sup>D</sup> <sup>∂</sup>*<sup>2</sup>

This equation is a 3-D, unsteady equation that applies to all flow conditions: laminar and turbulent. Since we cannot determine the instantaneous velocity field, the x-y-and z momentum equations were time averaged and hence were only able to practically predict the temporal mean velocity. Similarly, we time average the conservation of mass/heat equation using time averages of the velocity field.

The instantaneous velocity and concentration are decomposed into a mean and an unsteady component. Similar to the velocity field shown earlier, for concentration, c,

*<sup>t</sup> cdt* and *c*<sup>0</sup>

*c ∂x*<sup>2</sup> � �

þ

*∂*2 *c ∂y*<sup>2</sup> � �


� � � �

þ

*∂*2 *c ∂z*<sup>2</sup>

], S is the sources and sinks of reactions

].

is the fluctuation about the mean.

þ *S* |{z} sources*=*sinks (5)

*ρ ∂p <sup>∂</sup><sup>z</sup>* ¼ �*g*.

The conservation of constituent mass in a control volume is a sum of all the fluxes (advective and diffusive) into and out from the control volume plus sources and sinks (chemistry, biology, physics, withdrawals, inputs) within the control volume. Summing up the fluxes in each direction, assuming that the fluid is incompressible and that the molecular diffusivity, D, is homogeneous and isotropic, the

acting in z direction on the y-face of control volume, *τzz* ¼ *ρw*<sup>0</sup>

*v*0

turbulent shear stresses are often parameterized as *<sup>τ</sup>zx* <sup>¼</sup> *<sup>μ</sup>turbulent*�*zx <sup>∂</sup><sup>w</sup>*

, *<sup>τ</sup>zz* <sup>¼</sup> *<sup>μ</sup>turbulent*�*zz <sup>∂</sup><sup>w</sup>*

*w*0

Ð *z*

*∂v <sup>∂</sup><sup>x</sup>* ¼ *ρv*<sup>0</sup>

. The pressure is usually

*∂*2 *w ∂y*<sup>2</sup> þ

*v*<sup>0</sup> where τzy is the turbulent shear stress

� �

*ρ ∂p <sup>∂</sup><sup>y</sup>* ¼ � <sup>1</sup> *ρ ∂pa <sup>∂</sup><sup>y</sup>* <sup>þ</sup> *<sup>g</sup> <sup>∂</sup><sup>η</sup>*

*∂*2 *w ∂x*<sup>2</sup> þ

� �

*u*<sup>0</sup> where τzx is the turbulent shear stress acting in z direction on

*<sup>∂</sup><sup>z</sup>* ¼ *ρw*<sup>0</sup>

*w*0

*u*0 , *τyy* ¼

*<sup>η</sup> ρdz*, and the pressure gradient in

*∂*2 *w ∂z*<sup>2</sup>

*<sup>∂</sup><sup>y</sup>* � *<sup>g</sup> ρ* Ð *z η ∂ρ <sup>∂</sup><sup>y</sup> dz*.

*w*<sup>0</sup> where τzz is the

*<sup>∂</sup><sup>x</sup>* ¼ *ρw*<sup>0</sup>

. In cases where vertical

*u*0 ,

(4)

shear stresses are often parameterized as *τyx* ¼ *μturbulent*�*yx*

, *<sup>τ</sup>yz* <sup>¼</sup> *<sup>μ</sup>turbulent*�*xz <sup>∂</sup><sup>v</sup>*

the y-momentum then becomes after simplification � <sup>1</sup>

decomposed into the following terms: *p* ¼ *pa* þ *g*

*μturbulent*�*yy*

*∂v <sup>∂</sup><sup>y</sup>* ¼ *ρv*<sup>0</sup> *v*0

*Inland Waters - Dynamics and Ecology*

*2.1.4 Z-momentum equation*

*∂w ∂t* þ *u ∂w ∂x* þ *v ∂w ∂y* þ *w ∂w*

where: *τzx* ¼ *ρw*<sup>0</sup>

*τzy* ¼ *μturbulent*�*zy*

**equation**

*∂c ∂t* |{z} unsteady change in concentration

**108**

the x-face of control volume, *τzy* ¼ *ρw*<sup>0</sup>

*∂w <sup>∂</sup><sup>y</sup>* ¼ *ρw*<sup>0</sup>

reduced to the hydrostatic equation, i.e., <sup>1</sup>

advective diffusion equation becomes

<sup>þ</sup> *<sup>u</sup> <sup>∂</sup><sup>c</sup> <sup>∂</sup><sup>x</sup>* <sup>þ</sup> *<sup>v</sup>*

this becomes *<sup>c</sup>* <sup>¼</sup> *<sup>c</sup>* <sup>þ</sup> *<sup>c</sup>*<sup>0</sup> where *<sup>c</sup>* <sup>¼</sup> <sup>1</sup>

where c is the concentration [M/L�<sup>3</sup>

*∂c ∂y*


<sup>þ</sup> *<sup>w</sup> <sup>∂</sup><sup>c</sup> ∂z*

occurring in the control volume, or the reaction rate [ML�<sup>3</sup> T�<sup>1</sup>

*T* Ð*<sup>t</sup>*þ*<sup>T</sup>*

Substituting the time average and fluctuating components of concentration and velocities into the 3D governing equation and time averaging we obtain:

where the turbulent mass fluxes in x, y and z were assumed to be defined as a gradient, diffusion-type process, such as *u*´´*c* � � ¼ �*Ex <sup>∂</sup><sup>c</sup> <sup>∂</sup>x*, *v*´´*c* � � ¼ �*Ey ∂c ∂y* , *w*´ ´*c* � � <sup>¼</sup> �*Ez <sup>∂</sup><sup>c</sup> ∂z* , Ex is the turbulent mass diffusivity in x [L<sup>2</sup> /T], Ey is the turbulent mass diffusivity in y[L2 /T], Ez is the turbulent mass diffusivity in z [L<sup>2</sup> /T]. The new terms in the governing equation represent mass transport by turbulent eddies. As the intensity of turbulence increases, turbulent mass transport increases.

In turbulent fluids, Ex, Ey, and Ez >> D, and D can be neglected (except at boundaries or density interfaces where turbulent intensity may approach zero). The turbulent diffusion coefficients can be thought of as the product of the velocity scale of turbulence and the length scale of that turbulence. These coefficients are related to the turbulent eddy viscosity. In general, these turbulent diffusion coefficients are non-isotropic and non-homogeneous.

Spatial averaging of this equation leads to the introduction of "dispersion" coefficients which account for the transport of mass as a result of spatial irregularities in the velocity field.

These equations are also valid for heat transport and temperature modeling by substituting the concentration of heat, *ρcpT*, where T is temperature, cp is the coefficient of specific heat at constant pressure and ρ is the density, such that the governing equation for temperature, T, becomes after simplification

where DT is the molecular thermal conductivity for heat and Ex, Ey, and Ez are the heat and mass turbulent eddy diffusivities assuming they are of the same order of magnitude.

#### **2.3 Equation of state**

Since density is an important variable for the momentum equation to account for density-driven flows, the computation of density is accomplished through an equation of state where density is computed from dissolved and suspended solids concentrations (*cdissolved solids*,*csuspended solids*Þ and temperature, T, such as

$$\overline{\rho} = f\left(\overline{T}, \overline{\circledast\_{disolved\text{ solids}}}, \overline{\circledast\_{superplied\text{ solids}}}\right) \tag{8}$$

Typical assumptions of the flow field and water quality model are related to the dimensionality of the system (one, two or three-dimensions), whether the flow field is dynamic or steady-state, and the turbulence closure approximation. Based on the model assumptions, the model grid is developed where the governing equations are satisfied at points (differential equation representation) or over control volumes (integral representation). The resulting equations are then solved using

The source-sink term in the mass and heat conservation equation can be either positive or negative and is determined by each water quality state variable. The

quality state variables. Details of these can be found in Wells [20] and Chapra [23].

*<sup>S</sup>* <sup>¼</sup> <sup>0</sup> No sources and sinks

/s. **Table 1** shows some of the typical source sink terms for several water

*<sup>∂</sup><sup>z</sup>* <sup>φ</sup> is the heat flux in units of W/m<sup>2</sup>

*<sup>∂</sup><sup>z</sup>* wss is the settling velocity of

*∂calgae ∂z*

downward.

/s and in the heat balance equation the units are [Energy L�<sup>3</sup> T�<sup>1</sup>

**Typical source-sink term Description**

] with a typical unit of

transmitted through the water body. This is the short-wave solar radiation transmitted through the water and is a function of light extinction. The variable z is assumed to be positive

particles as a positive velocity, cSS is the concentration of suspended solids of a given size fraction. Often multiple size fractions are modeled independently using Stokes' law for settling velocity, wss. The variable z is assumed to be positive downward.

Source/sink terms are shown for dissolved CBOD (cCBODd) and particulate CBOD (cCBODp), kCBOD is a BOD decay rate for dissolved and particulate CBOD, and wCBOD is the settling velocity for particulate BOD. Models of CBOD usually use CBODultimate. Many models also track the P and N associated with this organic matter. Many models track multiple CBOD groups.

Source sink terms include the algae

] the "dark"

] (this is a

] the

growth rate μgrowth [T�<sup>1</sup>

μrespiration [T�<sup>1</sup>

complicated function of light, limiting nutrient and temperature),

respiration rate, μexcretion [T�<sup>1</sup>

rate of excretion or biomass loss,

] with a typical

numerical methods.

g/m3

unit of J/m3

**State variable**

Salinity or conservative substance

Suspended solids

**111**

*SSS* ¼ �*wSS <sup>∂</sup>cSS*

CBOD *Sparticulate* ¼ �*kCBODpcCBODp* �*wCBOD <sup>∂</sup>cCBODp ∂z Sdissolved* ¼ �*kCBODdcCBODd*

Algae *Salgae* <sup>¼</sup> *<sup>μ</sup>growthcalgae* � *<sup>μ</sup>respirationcalgae*

� *μexcretioncalgae* � *μmortalitycalgae* � *walgae*

Temperature *<sup>S</sup>* ¼ � *<sup>∂</sup><sup>φ</sup>*

**2.5 Sources-sinks for water quality and temperature**

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

units of *S* in the mass conservation equation are [ML�<sup>3</sup> T�<sup>1</sup>

Typical equations of state for fresh and saltwater have been published by Gill [8] and Ford and Johnson [9].

#### **2.4 Solution of governing equations**

There are six equations (continuity or conservation of fluid mass, conservation of momentum in x, y and z, and conservation of constituent mass or heat, equation of state) that we are solving for six unknowns: turbulent time average concentration (or temperature), velocities in x, y, and z, density and turbulent time average pressure (or water surface), i.e. *c or T*, *u*, *v*, *w*, ρ, *and η* or *p* . The mathematical solution is dependent on specifying the following: (1) turbulent shear stresses or Reynolds stresses by specification of the turbulent eddy viscosities, (2) turbulent mass (heat) fluxes by specification of Ex, Ey and Ez, (3) initial and boundary conditions, (4) dynamic molecular viscosity and molecular diffusivity for computations at interfaces or boundaries (otherwise, they are usually neglected since all natural water bodies are highly turbulent), and (5) the Coriolis acceleration (if 2D horizontal or 3D for large water bodies).

Determination of the turbulent eddy viscosities and eddy diffusivities is often based on what are termed closure models that are based on the turbulent Schmidt number (Sc ¼ ratio of turbulent viscosity to turbulent diffusivity of mass) and the turbulent Prandtl number (Pr ¼ ratio of turbulent viscosity to turbulent conductivity of heat). Most experimental evidence suggests that the turbulent Sc and Pr numbers are close to unity for turbulent flows and that turbulent Sc or Pr numbers vary only little between flows. Even though many models use a constant value of these ratios such that mass and heat transfer turbulent coefficients are approximately equal, buoyancy affects that value [10–12].

Determination of turbulent eddy viscosities have been based on multiple approaches: (1) eddy viscosity models as a function of water stability [13–16], (2) Mixing length models [17, 18], (3) One equation models for turbulent kinetic energy [19], (4) Two-equation k-ε models for turbulent kinetic energy and dissipation [11] and (5) Reynolds stress and algebraic stress models [11]. In many models, once the turbulent eddy viscosity is known, then the turbulent diffusion coefficients are computed from *<sup>E</sup>* � *<sup>μ</sup>turbulent <sup>ρ</sup>* where the approximation is based on typical Sc or Pr numbers. Many water quality and temperature models for lakes and reservoirs use some form of a k-ε turbulence model [20].

Vertical boundary conditions for the hydrodynamic model usually involve a surface shear stress condition for the wind and a bottom shear stress condition for frictional resistance based on a specified friction coefficient (for example, Chezy or Manning's). Vertical boundary conditions for temperature and water quality constituents are assumed to be known fluxes at the surface and bottom.

Horizontal boundary conditions for mass or heat include mass or heat fluxes as a result of advection and for hydrodynamics include water level (or head) or flow conditions. The flow conditions in outlets to stratified reservoirs can be complicated because of local vertical accelerations in the vicinity of the outlet. In many models, the vertical acceleration of a fluid parcel is assumed to be much less than the horizontal accelerations and hence the vertical momentum equation simplifies to the hydrostatic equation. In order to model the complicated outlet hydraulics in a reservoir, special selective withdrawal algorithms are often used [21, 22]. These allow the computation of flow from multiple vertical layers without having to solve the full-vertical momentum equation.

*Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

*ρ* ¼ *f T*,*cdissolved solids*,*csuspended solids*

and Ford and Johnson [9].

**2.4 Solution of governing equations**

*Inland Waters - Dynamics and Ecology*

tal or 3D for large water bodies).

cients are computed from *<sup>E</sup>* � *<sup>μ</sup>turbulent*

the full-vertical momentum equation.

**110**

use some form of a k-ε turbulence model [20].

Typical equations of state for fresh and saltwater have been published by Gill [8]

There are six equations (continuity or conservation of fluid mass, conservation of momentum in x, y and z, and conservation of constituent mass or heat, equation of state) that we are solving for six unknowns: turbulent time average concentration (or temperature), velocities in x, y, and z, density and turbulent time average pressure (or water surface), i.e. *c or T*, *u*, *v*, *w*, ρ, *and η* or *p* . The mathematical solution is dependent on specifying the following: (1) turbulent shear stresses or Reynolds stresses by specification of the turbulent eddy viscosities, (2) turbulent mass (heat) fluxes by specification of Ex, Ey and Ez, (3) initial and boundary conditions, (4) dynamic molecular viscosity and molecular diffusivity for computations at interfaces or boundaries (otherwise, they are usually neglected since all natural water bodies are highly turbulent), and (5) the Coriolis acceleration (if 2D horizon-

Determination of the turbulent eddy viscosities and eddy diffusivities is often based on what are termed closure models that are based on the turbulent Schmidt number (Sc ¼ ratio of turbulent viscosity to turbulent diffusivity of mass) and the turbulent Prandtl number (Pr ¼ ratio of turbulent viscosity to turbulent conductivity of heat). Most experimental evidence suggests that the turbulent Sc and Pr numbers are close to unity for turbulent flows and that turbulent Sc or Pr numbers vary only little between flows. Even though many models use a constant value of these ratios such that mass and heat transfer turbulent coefficients are

Determination of turbulent eddy viscosities have been based on multiple approaches: (1) eddy viscosity models as a function of water stability [13–16], (2) Mixing length models [17, 18], (3) One equation models for turbulent kinetic energy [19], (4) Two-equation k-ε models for turbulent kinetic energy and dissipation [11] and (5) Reynolds stress and algebraic stress models [11]. In many models, once the turbulent eddy viscosity is known, then the turbulent diffusion coeffi-

or Pr numbers. Many water quality and temperature models for lakes and reservoirs

Vertical boundary conditions for the hydrodynamic model usually involve a surface shear stress condition for the wind and a bottom shear stress condition for frictional resistance based on a specified friction coefficient (for example, Chezy or Manning's). Vertical boundary conditions for temperature and water quality constituents are assumed to be known fluxes at the surface and bottom.

Horizontal boundary conditions for mass or heat include mass or heat fluxes as a result of advection and for hydrodynamics include water level (or head) or flow conditions. The flow conditions in outlets to stratified reservoirs can be complicated because of local vertical accelerations in the vicinity of the outlet. In many models, the vertical acceleration of a fluid parcel is assumed to be much less than the horizontal accelerations and hence the vertical momentum equation simplifies to the hydrostatic equation. In order to model the complicated outlet hydraulics in a reservoir, special selective withdrawal algorithms are often used [21, 22]. These allow the computation of flow from multiple vertical layers without having to solve

*<sup>ρ</sup>* where the approximation is based on typical Sc

approximately equal, buoyancy affects that value [10–12].

(8)

Typical assumptions of the flow field and water quality model are related to the dimensionality of the system (one, two or three-dimensions), whether the flow field is dynamic or steady-state, and the turbulence closure approximation. Based on the model assumptions, the model grid is developed where the governing equations are satisfied at points (differential equation representation) or over control volumes (integral representation). The resulting equations are then solved using numerical methods.

#### **2.5 Sources-sinks for water quality and temperature**

The source-sink term in the mass and heat conservation equation can be either positive or negative and is determined by each water quality state variable. The units of *S* in the mass conservation equation are [ML�<sup>3</sup> T�<sup>1</sup> ] with a typical unit of g/m3 /s and in the heat balance equation the units are [Energy L�<sup>3</sup> T�<sup>1</sup> ] with a typical unit of J/m3 /s. **Table 1** shows some of the typical source sink terms for several water quality state variables. Details of these can be found in Wells [20] and Chapra [23].



**3. Lake and reservoir water quality models**

PO4-P *SPO*<sup>4</sup> <sup>¼</sup> *<sup>δ</sup>aP* �*μgrowthcalgae* <sup>þ</sup> *<sup>μ</sup>respirationcalgae* þ *δCBODdPkCBODdcCBODd*

þ *δCBODpPkCBODpcCBODp* þ *SODP*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

represent macrophytes).

**113**

**State variable**

**Table 1.**

There are many models used to simulate reservoir and lake water quality. A summary of modeling approaches for lakes is shown in Mooij et al. [24] and Janssen et al. [25]. **Table 2** shows a listing of some common lake and reservoir models. The choice of a correct framework is dependent on several considerations: (1) dimensionality of the lake/reservoir system (even though all water bodies are in essence 3D, 2D and 1D models can often represent the important processes of water quality and temperature gradients), (2) documentation (up-to-date user manual with example problems), (3) ease of use and expertise required (all models require a degree of file manipulation and many include GUI interfaces that often facilitate running the model for new users), (4) established record of successful projects (as documented in papers and conference proceedings and technical reports) and (5) model processes represent important lake/reservoir processes (for example, if macrophyte growth is an important ecological consideration, does the model

*Typical source-sink terms for temperature and some eutrophication water quality state variables.*

**Typical source-sink term Description**

*A V*

under anoxic conditions only (where kdenit is the denitrification rate under anoxic conditions). Other models also include terms for diffusion of nitrate into bottom muds. cNOX is the concentration of nitrite and

The source/sink terms shown include algae uptake and release (where δaP is the stoichiometric equivalent of algae to P), organic matter release as particulate and dissolved CBOD decay (where δCBODdP is the stoichiometric equivalent of cCBODd to P and δCBODpP is the stoichiometric equivalent of cCBODp to P), and sediment oxygen demand release under anoxic conditions (where SODP is the rate of P release in mass/ area/time and V is the volume of the computational cell, calgae is the algae concentration, and A is the area of the sediment). Other models include adsorption of P onto inorganic

nitrate.

particles.

In many cases, 3D models do not often do better than other model frameworks.

One reason may be that the data and parameter uncertainty increase in higher dimensional models [34]. In a comparison of 2D and 3D models, many examples have shown [28, 35, 36] that 2D models often better represent temperature profiles than some 3D models. There may be many reasons for this, but the important message is that more complicated models do not necessarily mean better model predictions. Another issue with 3D models is the excessive computational time compared to lower dimensional models. In one comparison between a 2D and 3D


**Table 1.**

**State variable**

Dissolved oxygen

Nitrate-Nitrite-N

**112**

**Typical source-sink term Description**

þ *δCBODdNkCBODdcCBODd* þ *δCBODpNkCBODpcCBODp*

Ammonia-N *Sammonia* <sup>¼</sup> *<sup>δ</sup>aN* �*μgrowthcalgae* <sup>þ</sup> *<sup>μ</sup>respirationcalgae*

*<sup>V</sup>* � *knitrcammonia*

*SDO* ¼ *δaO*<sup>2</sup> *μgrowthcalgae* � *μrespirationcalgae*

� *δNO*2*knitrcammonia* þ *kreaeraton*ð Þ *cs* � *cDO*

*SNOx* ¼ *knitrcammonia* � *δaNOx μgrowthcalgae* 

� *kCBODdcCBODd* � *kCBODpcCBODp* � *SOD <sup>A</sup>*

� *kdenitcNOx*

*V*

þ *SODN A*

*Inland Waters - Dynamics and Ecology*

μmortality [T�<sup>1</sup>

(which often can include zooplankton grazing as a separate loss rate based on zooplankton populations and zooplankton food preferences), and walgae the algae settling rate (this also can have complicated expressions especially for cyanobacteria and other species which migrate up and down in the water column). Often models include multiple algae groups. Calgae is the concentration of algae.

The source/sink terms shown include algae uptake and release (where δaN is the stoichiometric equivalent of algae to ammonia-N, but the N source can be nitrate), organic matter release as particulate and dissolved CBOD decay (where δCBODdN is the stoichiometric equivalent of cBODd to N and δCBODpN is the stoichiometric equivalent of cCBODp to N), and sediment oxygen demand release under anoxic conditions (where SODN is the rate of N release in mass/area/time and V is the volume of the computational cell and A is the area of the sediment), nitrification

decay rate knitr [T�<sup>1</sup>

the total ammonia concentration.

The source/sink term includes algae production and respiration (where δaO2 is the stoichiometric equivalent of dissolved oxygen to algae), CBOD particulate and dissolved watercolumn decay, sediment oxygen demand, nitrification demand (where δNO2 is the stoichiometric equivalent of dissolved oxygen to N), and reaeration at the surface only (where kreaeration is the reaeration rate in [T�<sup>1</sup>

generally a function of wind speed in lake and reservoirs and cs is the saturation value of dissolved oxygen). Other models also include terms for metal oxidation, methane oxidation, and oxidation of hydrogen sulfide.

The source/sink terms include algae uptake (where δaNOx is the stoichiometric equivalent of algae to nitrate-N since each algal group can have a preference for ammonia or nitrate as a N source), nitrification source, and a denitrification rate

], and cammonia is

] which is

] the mortality rate

*Typical source-sink terms for temperature and some eutrophication water quality state variables.*

#### **3. Lake and reservoir water quality models**

There are many models used to simulate reservoir and lake water quality. A summary of modeling approaches for lakes is shown in Mooij et al. [24] and Janssen et al. [25]. **Table 2** shows a listing of some common lake and reservoir models.

The choice of a correct framework is dependent on several considerations: (1) dimensionality of the lake/reservoir system (even though all water bodies are in essence 3D, 2D and 1D models can often represent the important processes of water quality and temperature gradients), (2) documentation (up-to-date user manual with example problems), (3) ease of use and expertise required (all models require a degree of file manipulation and many include GUI interfaces that often facilitate running the model for new users), (4) established record of successful projects (as documented in papers and conference proceedings and technical reports) and (5) model processes represent important lake/reservoir processes (for example, if macrophyte growth is an important ecological consideration, does the model represent macrophytes).

In many cases, 3D models do not often do better than other model frameworks. One reason may be that the data and parameter uncertainty increase in higher dimensional models [34]. In a comparison of 2D and 3D models, many examples have shown [28, 35, 36] that 2D models often better represent temperature profiles than some 3D models. There may be many reasons for this, but the important message is that more complicated models do not necessarily mean better model predictions. Another issue with 3D models is the excessive computational time compared to lower dimensional models. In one comparison between a 2D and 3D


#### **Table 2.**

*List of common lake and reservoir water quality models.*

model, the 3D model took 30 longer than the 2D model. This will vary depending on model configuration and model. This is becoming more of an issue as models are being used for multiple-decade simulations evaluating climate change and longterm changes in model boundary conditions.

#### **4. Typical results of lake and reservoir modeling**

Using the CE-QUAL-W2 model [20] as an example, consider an application to Folsom Reservoir, CA, USA, as presented in Martinez et al. [37].

Folsom lake, located near Sacramento California USA, is a deep-storage reservoir that provides municipal water, power generation and cold water for primarily salmonid fish in the lower American River (see **Figure 10**). The reservoir has multiple outlets that allow the operator to choose different water levels for downstream temperature control.

The model was set-up and calibrated to a 10-year period between January 1, 2001 and December 31, 2011. Boundary conditions for flow, meteorological data, and outflow during this period were developed. A very detailed approach for filling in data gaps was undertaken to provide a good set of boundary conditions. Typical model predictions compared to field data are shown for temperature in **Figure 11** in 2002 and 2007 at multiple longitudinal stations in the reservoir. Error statistics for temperature profiles over the 10-year period using about 27,000 data comparisons were an average mean error of 0.004°C, an average absolute mean error (AME, average absolute value of the error) of 0.56°C, and a root mean square (RMS) average error of 0.71°C. The R<sup>2</sup> correlation between modeled and predicted temperature was 0.996.

In other examples of predicting the thermal regime, Cole [38] has shown that typical errors (AME, RMS) for temperature should often be well less than 1°C with a mean error of close to zero with minimal calibration if the boundary condition data are well-specified.

higher elevation pristine lake, Chester Morse Lake, WA, USA, Ceravich and Wells [39] have shown dissolved oxygen profiles mimicking the unusual behavior of the dissolved oxygen profile in a lake with little algae growth as shown in **Figure 12**. Error statistics for dissolved oxygen, which integrates all the water quality

*Folsom reservoir model temperature predictions compared to field data on August 20, 2002 (left) and October*

*Folsom reservoir bathymetry showing the north fork and south fork of the American River channels. Axes are*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

**Figure 10.**

*labeled in m.*

**Figure 11.**

**115**

*31, 2007 (right) at 6 different stations in Folsom reservoir.*

Oftentimes, the success of modeling other water quality state variables is first dependent on obtaining good temperature calibration results. For example, in a

*Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

model, the 3D model took 30 longer than the 2D model. This will vary depending on model configuration and model. This is becoming more of an issue as models are being used for multiple-decade simulations evaluating climate change and long-

**Model name Description Reference**

temperature and water quality models

CE-QUAL-W2 2D longitudinal-vertical, open source,

quality solved together

W3 3D, hydrodynamics and water quality solved

EFDC and WASP 3D, hydrodynamics and water quality solved

together

models

1D model based on mixed layer dynamics, separate

eutrophication model, hydrodynamics and water

CE-QUAL-R1 1D vertical Environmental

separately, both sigma stretch and z coordinate

GLM 1D Hipsey et al. [31]

3D-mixed layer dynamic model, hydrodynamics

and water quality solved separately

Tanentzap et al. [26]

Wells [20]

Laboratory [27]

[28]

[30]

Al-Zubaidi and Wells

Hamrick [29], Tetra Tech

Hipsey et al. [32], Hodges and Dallimore [33]

Using the CE-QUAL-W2 model [20] as an example, consider an application to

Folsom lake, located near Sacramento California USA, is a deep-storage reservoir

that provides municipal water, power generation and cold water for primarily salmonid fish in the lower American River (see **Figure 10**). The reservoir has multiple outlets that allow the operator to choose different water levels for down-

The model was set-up and calibrated to a 10-year period between January 1, 2001 and December 31, 2011. Boundary conditions for flow, meteorological data, and outflow during this period were developed. A very detailed approach for filling in data gaps was undertaken to provide a good set of boundary conditions. Typical model predictions compared to field data are shown for temperature in **Figure 11** in 2002 and 2007 at multiple longitudinal stations in the reservoir. Error statistics for temperature profiles over the 10-year period using about 27,000 data comparisons were an average mean error of 0.004°C, an average absolute mean error (AME, average absolute value of the error) of 0.56°C, and a root mean square (RMS) average error of 0.71°C. The R<sup>2</sup> correlation between modeled and predicted tem-

In other examples of predicting the thermal regime, Cole [38] has shown that typical errors (AME, RMS) for temperature should often be well less than 1°C with a mean error of close to zero with minimal calibration if the boundary condition

Oftentimes, the success of modeling other water quality state variables is first dependent on obtaining good temperature calibration results. For example, in a

term changes in model boundary conditions.

*List of common lake and reservoir water quality models.*

stream temperature control.

DYRESM and CAEDYM

*Inland Waters - Dynamics and Ecology*

ELCOM and CAEDYM

**Table 2.**

perature was 0.996.

data are well-specified.

**114**

**4. Typical results of lake and reservoir modeling**

Folsom Reservoir, CA, USA, as presented in Martinez et al. [37].

*Folsom reservoir bathymetry showing the north fork and south fork of the American River channels. Axes are labeled in m.*

#### **Figure 11.**

*Folsom reservoir model temperature predictions compared to field data on August 20, 2002 (left) and October 31, 2007 (right) at 6 different stations in Folsom reservoir.*

higher elevation pristine lake, Chester Morse Lake, WA, USA, Ceravich and Wells [39] have shown dissolved oxygen profiles mimicking the unusual behavior of the dissolved oxygen profile in a lake with little algae growth as shown in **Figure 12**. Error statistics for dissolved oxygen, which integrates all the water quality

processes, were a ME of 0.15 mg/l, a AME of 0.42 mg/l, and a RMS error of 0.49 mg/l for 551 data-model comparisons.

#### **5. Conclusions in hydrodynamic and water quality modeling**

The complexity of existing models has often exceeded our capacity in the field to verify model coefficients usually because of cost and time. Deterministic water quality models require an incredible amount of information that is rarely measured. In the CE-QUAL-W2 model, for each algal group the model user must specify approximately 25 values describing rate coefficients for growth, respiration, excretion, mortality, stoichiometry, temperature preferences, N preferences, light saturation limits, and settling velocities. Even though this model has no limit to the number of algal groups one can represent mathematically, in a practical sense modeling living populations and their impact on nutrients, organic matter, pH, temperature, and oxygen is very complex. In the end, the model user tries to balance the known field data with literature values of the coefficients with the goal that if the boundary conditions are well-specified, the model requires little calibration.

in ID/OR, USA, from Harrison [40]. The bacterial populations were modeled based on Reichert et al. [41] as shown in **Figure 13** and compared to a model with only a first order decay rate for organic matter decay (basically neglecting all the complex bacterial dynamics). In predicting the impact of organic matter on dissolved oxygen, the simpler model neglecting bacterial dynamics performed better. This does not mean that complex models may not be useful for research purposes, but more

Hence, to improve water quality models, one of the most fruitful areas is working on obtaining better boundary condition data by "smart" filling in of data gaps in time series of field data. This is still a critical component of modeling lakes and reservoirs. In addition, measuring field data on-site for lakes and reservoirs helps tremendously

in understanding better the impact of hydrodynamics on water quality.

*Bacterial dynamics model compartments in the Snake River from Harrison [40].*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

Department of Civil and Environmental Engineering, Portland State University,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

complicated does not mean a better model.

\*Address all correspondence to: wellss@pdx.edu

provided the original work is properly cited.

**Author details**

Scott A. Wells

**Figure 13.**

Portland, USA

**117**

If one cannot understand and interpret field data, then it will be challenging for a model to match field measurements. Hence, knowing and understanding the field data as one is setting up the model is important for making sure the model is agreeing with field data trends.

In other cases though, the model is able to discern complex interactions between water quality state variables that may be difficult for the model user to piece together a priori. For example, the unusual dissolved oxygen profiles in the field data and model shown in **Figure 12** is one example where it was unclear the reasons for the unusual vertical profile until the combination of a sharp thermocline, algae growth within the metalimnion, and slow sediment oxygen demand caused the model to match the field data vertical trend.

Water quality models are adding more and more complex algorithms to reproduce admittedly complex phenomena. But this increasing complexity does not necessarily mean a better model or one that better reproduces field data. One example is the use of a complex model of bacterial populations on the Snake River

#### **Figure 12.**

*Predictions (solid lines) and field data (dots) of dissolved oxygen at one sampling site for Chester Morse Lake in 2015. Dates shown are Julian days since January 1, 2015.*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

processes, were a ME of 0.15 mg/l, a AME of 0.42 mg/l, and a RMS error of

The complexity of existing models has often exceeded our capacity in the field to verify model coefficients usually because of cost and time. Deterministic water quality models require an incredible amount of information that is rarely measured. In the CE-QUAL-W2 model, for each algal group the model user must specify approximately 25 values describing rate coefficients for growth, respiration, excretion, mortality, stoichiometry, temperature preferences, N preferences, light saturation limits, and settling velocities. Even though this model has no limit to the number of algal groups one can represent mathematically, in a practical sense modeling living populations and their impact on nutrients, organic matter, pH, temperature, and oxygen is very complex. In the end, the model user tries to balance the known field data with literature values of the coefficients with the goal that if the boundary

If one cannot understand and interpret field data, then it will be challenging for a model to match field measurements. Hence, knowing and understanding the field data as one is setting up the model is important for making sure the model is

In other cases though, the model is able to discern complex interactions between

Water quality models are adding more and more complex algorithms to reproduce admittedly complex phenomena. But this increasing complexity does not necessarily mean a better model or one that better reproduces field data. One example is the use of a complex model of bacterial populations on the Snake River

*Predictions (solid lines) and field data (dots) of dissolved oxygen at one sampling site for Chester Morse Lake in*

water quality state variables that may be difficult for the model user to piece together a priori. For example, the unusual dissolved oxygen profiles in the field data and model shown in **Figure 12** is one example where it was unclear the reasons for the unusual vertical profile until the combination of a sharp thermocline, algae growth within the metalimnion, and slow sediment oxygen demand caused the

**5. Conclusions in hydrodynamic and water quality modeling**

conditions are well-specified, the model requires little calibration.

0.49 mg/l for 551 data-model comparisons.

*Inland Waters - Dynamics and Ecology*

agreeing with field data trends.

**Figure 12.**

**116**

model to match the field data vertical trend.

*2015. Dates shown are Julian days since January 1, 2015.*

**Figure 13.** *Bacterial dynamics model compartments in the Snake River from Harrison [40].*

in ID/OR, USA, from Harrison [40]. The bacterial populations were modeled based on Reichert et al. [41] as shown in **Figure 13** and compared to a model with only a first order decay rate for organic matter decay (basically neglecting all the complex bacterial dynamics). In predicting the impact of organic matter on dissolved oxygen, the simpler model neglecting bacterial dynamics performed better. This does not mean that complex models may not be useful for research purposes, but more complicated does not mean a better model.

Hence, to improve water quality models, one of the most fruitful areas is working on obtaining better boundary condition data by "smart" filling in of data gaps in time series of field data. This is still a critical component of modeling lakes and reservoirs. In addition, measuring field data on-site for lakes and reservoirs helps tremendously in understanding better the impact of hydrodynamics on water quality.

#### **Author details**

Scott A. Wells Department of Civil and Environmental Engineering, Portland State University, Portland, USA

\*Address all correspondence to: wellss@pdx.edu

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **References**

[1] Wetzel R. Limnology Lake and River Ecosystems. NY: Academic Press; 2001

[2] Hutchinson GE. A Treatise on Limnology. New York: John Wiley & Sons; 1967

[3] Martin J, Higgins J, Edinger J, Gordon J. Energy Production and Reservoir Water Quality. Reston, VA: ASCE; 2007

[4] Wells SA, Manson JR, Martin JL. Numerical hydrodynamic and transport models for reservoirs. In: Martin J, Higgins J, Edinger J, Gordon J, editors. Energy Production and Reservoir Water Quality. Reston, VA: ASCE; 2007. Chapter 4

[5] Batchelor GK. An Introduction to Fluid Dynamics. NY: Cambridge University Press; 1967

[6] Sabersky R, Acosta A, Haupmann E. Fluid Flow A First Course in Fluid Mechanics. NY: Macmillan Publishing Co.; 1989

[7] Cushman-Roisin B. Introduction to Geophysical Fluid Dynamics. Englewood Cliffs, NJ: Prentice-Hall; 1994

[8] Gill AE. "Appendix 3, Properties of Seawater", Atmosphere Ocean Dynamics. Vol. 599. New York, NY: Academic Press; 1982. p. 600

[9] Ford DE, Johnson MC. An Assessment of Reservoir Density Currents and Inflow Processes. Technical Rpt. E 83-7. Vicksburg, MS: US Army, Engineer Waterways Experiment Station; 1983

[10] Turner JS. Buoyancy Effects in Fluids. Cambridge: Cambridge University Press; 1973

[11] Rodi W. Turbulence models and their application in hydraulics. In:

IAHR. 3rd ed. Rotterdam: A.A. Balkema; 1993

Department of Civil and Environmental Engineering, Portland State University;

*DOI: http://dx.doi.org/10.5772/intechopen.91754*

*Modeling Thermal Stratification Effects in Lakes and Reservoirs*

[28] Al-Zubaidi HAM, Wells SA. Analytical and field verification of a 3D hydrodynamic and water quality numerical scheme based on the 2D formulation in CE-QUAL-W2. Journal of Hydraulic Research. 2020;**58**(1):

[29] Hamrick JM. A three-dimensional environmental fluid dynamics computer code: Theoretical and computational aspects. In: Special Report. Vol. **317**. The College of William and Mary, Virginia Institute of Marine Science; 1992. p. 63

[30] Tetra Tech. The Environmental Fluid Dynamics Code User Manual US EPA Version 1.01. Fairfax, VA; 2007

[31] Hipsey MR, Bruce LC, Hamilton DP. GLM—General lake model: Model overview and user information. In: AED Report #26. The University of Western Australia Technical Manual. 2014. p. 22

[32] Hipsey MR, Romero J, Antenucci J, Hamilton D. Computational Aquatic Ecosystem Dynamics Model CAEDYM v2.0 Science Manual. Centre for Water Research, University of Western

[33] Hodges B, Dallimore C. Estuary and Lake Computer Model Science Manual Code Version 1.5.0. University of Western Australia: Centre for Water

[34] EPA. Guidance on the development,

environmental models. In: EPA/100/K-09/003. Washington, DC: Office of the

evaluation, and application of

[35] DeGasperi C. Modeling Lake Sammamish, WA Using a 2-D and 3-D Model, Presentation. Portland State University: Department of Civil

[36] Geologic Survey Israel and Tahal. Red Sea Dead Sea Conveyance Study

Science Advisor; 2009

Engineering; 2005

Australia; 2003

Research; 2001

152-171. DOI: 10.1080/ 00221686.2018.1499051

[22] Davis JE, Holland JP, Schneider ML, Wilhelms SC. SELECT: A Numerical, One-Dimensional Model for Selective Withdrawal, Instruction Report E-87-2. Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, MS:

[23] Chapra S. Surface Water Quality Modeling. NY: McGraw-Hill; 1997

[24] Mooij WM, Trolle D, Jeppesen E, Arhonditsis G, Belolipetsky PV, Chitamwebwa DBR, et al. Challenges and opportunities for integrating lake ecosystem modelling approaches. Aquatic Ecology. 2010;**44**(3):633-667

[25] Janssen ABG, Arhonditsis GB, Beusen A, Bolding K, Bruce L,

and evolving diversity of aquatic ecosystem models: A community perspective. Aquatic Ecology. 2015; **49**(4):513-548. DOI: 10.1007/

[26] Tanentzap AJ, Hamilton DP, Yan ND. Calibrating the dynamic reservoir simulation model (DYRESM) and filling required data gaps for onedimensional thermal profile predictions

in a boreal lake. Limnology and Oceanography: Methods. 2007;**5**:

[27] Environmental Laboratory. CE-QUAL-R1: A Numerical One-Dimensional Model of Reservoir Water Quality: Users Manual, Technical Report

E-82-1. Vicksburg, MS: Corps of Engineers, Waterways Experiment Station, Environmental Laboratory; 1982

s10452-015-9544-1

484-494

**119**

Bruggeman J, et al. Exploring, exploiting

Corps of Engineers; 1987

[21] Brooks NH, Koh RC. Selective withdrawal from density-stratified reservoirs. Journal of Hydraulics Division, ASCE. 1969;**95**(HY4):

2019

1369-1397

[12] Venayagamoorthy SK, Koseff JR, Ferziger JH, Shih LH. Testing of RANS turbulence models for stratified flows based on DNS data. In: Annual Research Report Briefs. Center for Turbulence Research; 2003. pp. 127-138

[13] Munk WH, Anderson ER. Notes on the theory of the thermocline. Journal of Marine Research. 1948;**1**:276

[14] Mamayev OI. The influence of stratification on vertical turbulent mixing in the sea. Izv. Geophys. Ser. 1958:870-875

[15] Fischer HB, List J, Koh R, Imberger J, Brooks N. Mixing in Inland and Coastal Waters. New York: Academic Press; 1979

[16] Holland PR, Kay A, Botte V. A numerical study of the dynamics of the riverine thermal bar in a deep lake. Environmental Fluid Mechanics. 2001;**1**: 311-332

[17] Nezu I, Nakagawa H. Turbulence in Open-Channel Flows. Rotterdam: A.A. Balkema; 1993

[18] Bloss S, Patterson JC. Modeling turbulent transport in a stratified estuary. ASCE Journal of Hydraulic Engineering. 1988;**114**(9):1115-1133

[19] Martin JL, McCutcheon SC. Hydrodynamics and Transport for Water Quality Modeling. NY: Lewis Publishers; 1999

[20] Wells SA. CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 4.2, User Manual Part 2, Hydrodynamic and Water Quality Model Theory. Portland, OR:

*Modeling Thermal Stratification Effects in Lakes and Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.91754*

Department of Civil and Environmental Engineering, Portland State University; 2019

**References**

Sons; 1967

ASCE; 2007

Chapter 4

Co.; 1989

[1] Wetzel R. Limnology Lake and River Ecosystems. NY: Academic Press; 2001

IAHR. 3rd ed. Rotterdam: A.A. Balkema;

[12] Venayagamoorthy SK, Koseff JR, Ferziger JH, Shih LH. Testing of RANS turbulence models for stratified flows based on DNS data. In: Annual Research Report Briefs. Center for Turbulence

[13] Munk WH, Anderson ER. Notes on the theory of the thermocline. Journal of

Research; 2003. pp. 127-138

Marine Research. 1948;**1**:276

[15] Fischer HB, List J, Koh R,

and Coastal Waters. New York:

[16] Holland PR, Kay A, Botte V. A numerical study of the dynamics of the riverine thermal bar in a deep lake. Environmental Fluid Mechanics. 2001;**1**:

[17] Nezu I, Nakagawa H. Turbulence in Open-Channel Flows. Rotterdam: A.A.

[18] Bloss S, Patterson JC. Modeling turbulent transport in a stratified estuary. ASCE Journal of Hydraulic Engineering. 1988;**114**(9):1115-1133

[19] Martin JL, McCutcheon SC. Hydrodynamics and Transport for Water Quality Modeling. NY: Lewis

[20] Wells SA. CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 4.2, User Manual Part 2, Hydrodynamic and Water Quality Model Theory. Portland, OR:

Academic Press; 1979

Imberger J, Brooks N. Mixing in Inland

1958:870-875

311-332

Balkema; 1993

Publishers; 1999

[14] Mamayev OI. The influence of stratification on vertical turbulent mixing in the sea. Izv. Geophys. Ser.

1993

[2] Hutchinson GE. A Treatise on Limnology. New York: John Wiley &

*Inland Waters - Dynamics and Ecology*

[3] Martin J, Higgins J, Edinger J, Gordon J. Energy Production and Reservoir Water Quality. Reston, VA:

[4] Wells SA, Manson JR, Martin JL. Numerical hydrodynamic and transport models for reservoirs. In: Martin J, Higgins J, Edinger J, Gordon J, editors. Energy Production and Reservoir Water Quality. Reston, VA: ASCE; 2007.

[5] Batchelor GK. An Introduction to Fluid Dynamics. NY: Cambridge

[6] Sabersky R, Acosta A, Haupmann E. Fluid Flow A First Course in Fluid Mechanics. NY: Macmillan Publishing

[7] Cushman-Roisin B. Introduction to Geophysical Fluid Dynamics. Englewood

[8] Gill AE. "Appendix 3, Properties of

Cliffs, NJ: Prentice-Hall; 1994

Seawater", Atmosphere Ocean Dynamics. Vol. 599. New York, NY: Academic Press; 1982. p. 600

[9] Ford DE, Johnson MC. An Assessment of Reservoir Density Currents and Inflow Processes. Technical Rpt. E 83-7. Vicksburg, MS: US Army, Engineer Waterways Experiment Station; 1983

[10] Turner JS. Buoyancy Effects in Fluids. Cambridge: Cambridge

[11] Rodi W. Turbulence models and their application in hydraulics. In:

University Press; 1973

**118**

University Press; 1967

[21] Brooks NH, Koh RC. Selective withdrawal from density-stratified reservoirs. Journal of Hydraulics Division, ASCE. 1969;**95**(HY4): 1369-1397

[22] Davis JE, Holland JP, Schneider ML, Wilhelms SC. SELECT: A Numerical, One-Dimensional Model for Selective Withdrawal, Instruction Report E-87-2. Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, MS: Corps of Engineers; 1987

[23] Chapra S. Surface Water Quality Modeling. NY: McGraw-Hill; 1997

[24] Mooij WM, Trolle D, Jeppesen E, Arhonditsis G, Belolipetsky PV, Chitamwebwa DBR, et al. Challenges and opportunities for integrating lake ecosystem modelling approaches. Aquatic Ecology. 2010;**44**(3):633-667

[25] Janssen ABG, Arhonditsis GB, Beusen A, Bolding K, Bruce L, Bruggeman J, et al. Exploring, exploiting and evolving diversity of aquatic ecosystem models: A community perspective. Aquatic Ecology. 2015; **49**(4):513-548. DOI: 10.1007/ s10452-015-9544-1

[26] Tanentzap AJ, Hamilton DP, Yan ND. Calibrating the dynamic reservoir simulation model (DYRESM) and filling required data gaps for onedimensional thermal profile predictions in a boreal lake. Limnology and Oceanography: Methods. 2007;**5**: 484-494

[27] Environmental Laboratory. CE-QUAL-R1: A Numerical One-Dimensional Model of Reservoir Water Quality: Users Manual, Technical Report E-82-1. Vicksburg, MS: Corps of Engineers, Waterways Experiment Station, Environmental Laboratory; 1982 [28] Al-Zubaidi HAM, Wells SA. Analytical and field verification of a 3D hydrodynamic and water quality numerical scheme based on the 2D formulation in CE-QUAL-W2. Journal of Hydraulic Research. 2020;**58**(1): 152-171. DOI: 10.1080/ 00221686.2018.1499051

[29] Hamrick JM. A three-dimensional environmental fluid dynamics computer code: Theoretical and computational aspects. In: Special Report. Vol. **317**. The College of William and Mary, Virginia Institute of Marine Science; 1992. p. 63

[30] Tetra Tech. The Environmental Fluid Dynamics Code User Manual US EPA Version 1.01. Fairfax, VA; 2007

[31] Hipsey MR, Bruce LC, Hamilton DP. GLM—General lake model: Model overview and user information. In: AED Report #26. The University of Western Australia Technical Manual. 2014. p. 22

[32] Hipsey MR, Romero J, Antenucci J, Hamilton D. Computational Aquatic Ecosystem Dynamics Model CAEDYM v2.0 Science Manual. Centre for Water Research, University of Western Australia; 2003

[33] Hodges B, Dallimore C. Estuary and Lake Computer Model Science Manual Code Version 1.5.0. University of Western Australia: Centre for Water Research; 2001

[34] EPA. Guidance on the development, evaluation, and application of environmental models. In: EPA/100/K-09/003. Washington, DC: Office of the Science Advisor; 2009

[35] DeGasperi C. Modeling Lake Sammamish, WA Using a 2-D and 3-D Model, Presentation. Portland State University: Department of Civil Engineering; 2005

[36] Geologic Survey Israel and Tahal. Red Sea Dead Sea Conveyance Study

Program. GSI Report Number: GSI/10/ 2011. Israel, Jerusalem; 2011

**Chapter 8**

**Abstract**

purposes in NEB.

**1. Introduction**

**121**

rain gauge, ground-based validation

Assessment of the CHIRPS-Based

Satellite Precipitation Estimates

*Manoj Kumar Thakur and Catarina de Oliveira Buriti*

At present, satellite rainfall products, such as the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) product, have become an alternative source of rainfall data for regions where rain gauge stations are sparse, e.g., Northeast Brazil (NEB). In this study, continuous scores (i.e., Pearson's correlation coefficient, R; percentage bias, PBIAS; and unbiased root mean square error, ubRMSE) and categorical scores (i.e., probability of detection, POD; false alarm ratio, FAR; and threat score, TS) were used to assess the CHIRPS rainfall estimates against ground-based observations on a pixel-to-station basis, during 01 January 1981 to 30 June 2019 over NEB. Results showed that CHIRPS exhibits better performance in inland regions (R, PBIAS, and ubRMSE median: 0.51, �3.71%, and 9.20 mm/day; POD, FAR, and TS median: 0.59, 0.44, and 0.40, respectively) than near the coast (R, PBIAS, and ubRMSE median: 0.36, �5.66%, and 12.43 mm/day; POD, FAR, and TS median: 0.32, 0.42, and 0.26, respectively). It shows better performance in the wettest months (i.e., DJF) than in the driest months (i.e., JJA) and is sensitive to both the warm-top stratiform cloud systems and the sub-cloud evaporation processes. Overall, the CHIRPS rainfall data set could be used for some operational

**Keywords:** CHIRPS, Northeast Brazil, satellite rainfall, rainfall, remote sensing,

Rainfall is a key component of the global water cycle and is essential for a wide range of applications such as crop modeling, hydrometeorology, water resource management, flood and drought monitoring, and climatological applications [1–3]. Accurate and consistent rainfall estimates are also of remarkable importance for the drought-prone regions, such as the semiarid region of Northeast Brazil (NEB), which is at high risk of food insecurity due to the occurrence of prolonged droughts whose impacts affect adversely their water resources and crop production [4–6]. Nowadays, the measurement of precipitation is based on rain gauge stations, meteorological radars, and satellite retrievals [7, 8]. Rainfall data from ground stations provide high accuracy [9], but they are limited in spatial coverage [10]. Meteorological radars suffer from reduced data quality owing to signal blockage or

*Franklin Paredes-Trejo, Humberto Alves Barbosa,*

*Tumuluru Venkata Lakshmi Kumar,*

[37] Martinez VI, Wells SA, Addley RC. Meeting temperature requirements for fisheries downstream of Folsom Reservoir, California. In: EWRI, ASCE, Portland, OR: Proceedings World Environmental and Water Resources Congress. 2014. pp. 1081-1092

[38] Cole T. Examples of model applications. In: Wells S, editor. CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 4.2, User Manual Part 4, Model Examples. Portland, OR: Department of Civil and Environmental Engineering, Portland State University; 2019

[39] Ceravich A, Wells SA. Water quality and hydrodynamic modeling of Chester Morse Lake. In: Technical Report Prepared for Seattle Public Utilities. WA, Seattle: Department of Civil and Environmental Engineering, Portland State University; 2020

[40] Harrison J. Partitioning snake river organic matter and modeling aerobic oxidation. Brownlee Reservoir [PhD dissertation]. Idaho: Department of Civil Engineering, University of Idaho; 2005

[41] Reichert P, Borchardt D, Henze M, Rauch W, Shanahan P, Somlyody L, et al. River water quality model no. 1. In: IWA Task Group on River Water Quality Modeling, editor. Scientific and Technical Report No. 12. London, UK: IWA Publishing; 2001. p. 131

#### **Chapter 8**

Program. GSI Report Number: GSI/10/

*Inland Waters - Dynamics and Ecology*

[37] Martinez VI, Wells SA, Addley RC. Meeting temperature requirements for fisheries downstream of Folsom Reservoir, California. In: EWRI, ASCE, Portland, OR: Proceedings World Environmental and Water Resources Congress. 2014. pp. 1081-1092

2011. Israel, Jerusalem; 2011

[38] Cole T. Examples of model applications. In: Wells S, editor. CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 4.2, User Manual Part 4, Model Examples. Portland, OR: Department of Civil and Environmental Engineering, Portland

State University; 2019

State University; 2020

2005

**120**

[39] Ceravich A, Wells SA. Water quality and hydrodynamic modeling of Chester Morse Lake. In: Technical Report Prepared for Seattle Public Utilities. WA, Seattle: Department of Civil and Environmental Engineering, Portland

[40] Harrison J. Partitioning snake river organic matter and modeling aerobic oxidation. Brownlee Reservoir [PhD dissertation]. Idaho: Department of Civil Engineering, University of Idaho;

[41] Reichert P, Borchardt D, Henze M, Rauch W, Shanahan P, Somlyody L, et al. River water quality model no. 1. In: IWA Task Group on River Water Quality Modeling, editor. Scientific and Technical Report No. 12. London, UK:

IWA Publishing; 2001. p. 131

### Assessment of the CHIRPS-Based Satellite Precipitation Estimates

*Franklin Paredes-Trejo, Humberto Alves Barbosa, Tumuluru Venkata Lakshmi Kumar, Manoj Kumar Thakur and Catarina de Oliveira Buriti*

#### **Abstract**

At present, satellite rainfall products, such as the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) product, have become an alternative source of rainfall data for regions where rain gauge stations are sparse, e.g., Northeast Brazil (NEB). In this study, continuous scores (i.e., Pearson's correlation coefficient, R; percentage bias, PBIAS; and unbiased root mean square error, ubRMSE) and categorical scores (i.e., probability of detection, POD; false alarm ratio, FAR; and threat score, TS) were used to assess the CHIRPS rainfall estimates against ground-based observations on a pixel-to-station basis, during 01 January 1981 to 30 June 2019 over NEB. Results showed that CHIRPS exhibits better performance in inland regions (R, PBIAS, and ubRMSE median: 0.51, �3.71%, and 9.20 mm/day; POD, FAR, and TS median: 0.59, 0.44, and 0.40, respectively) than near the coast (R, PBIAS, and ubRMSE median: 0.36, �5.66%, and 12.43 mm/day; POD, FAR, and TS median: 0.32, 0.42, and 0.26, respectively). It shows better performance in the wettest months (i.e., DJF) than in the driest months (i.e., JJA) and is sensitive to both the warm-top stratiform cloud systems and the sub-cloud evaporation processes. Overall, the CHIRPS rainfall data set could be used for some operational purposes in NEB.

**Keywords:** CHIRPS, Northeast Brazil, satellite rainfall, rainfall, remote sensing, rain gauge, ground-based validation

#### **1. Introduction**

Rainfall is a key component of the global water cycle and is essential for a wide range of applications such as crop modeling, hydrometeorology, water resource management, flood and drought monitoring, and climatological applications [1–3]. Accurate and consistent rainfall estimates are also of remarkable importance for the drought-prone regions, such as the semiarid region of Northeast Brazil (NEB), which is at high risk of food insecurity due to the occurrence of prolonged droughts whose impacts affect adversely their water resources and crop production [4–6].

Nowadays, the measurement of precipitation is based on rain gauge stations, meteorological radars, and satellite retrievals [7, 8]. Rainfall data from ground stations provide high accuracy [9], but they are limited in spatial coverage [10]. Meteorological radars suffer from reduced data quality owing to signal blockage or distortion [11]. Satellites can be used for sensing large regions with a high temporal and spatial resolution, though satellite retrieval approaches are prone to biases and systematic errors [12]. Consequently, satellite-based rainfall estimates must be validated against rain gauge data in order to assess their uncertainties before being used [13, 14].

(<500 mm/year) [22], due to the impact of the orography [26] and the influence of different meteorological systems, such as the intertropical convergence zone (ITCZ), squall lines (SL), easterly wave disturbances (EWD), upper tropospheric cyclonic vortices (UTCV), frontal systems (FS), mesoscale convective complexes (MCC), and the South Atlantic convergence zone (SACZ) [27]. The rainy season occurs at different times of the year: April to June in the eastern coast of the NEB; November to January in the southern part of the NEB; and March to May in the semiarid northwestern part of the NEB [27]. This region includes two main river basins, namely, the basins of the São Francisco River (where the Sobradinho reservoir is located) and the Parnaíba River. It also contains the Amazonia, Cerrado, Atlantic Forest, and Caatinga biomes, which are strongly related to the spatial

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

Daily rain gauge observations from rain gauge stations were provided by the INMET (www.inmet.gov.br). The higher values than daily mean 3.5 standard deviations (method for detection of outliers) were coded as missing data [20]. The daily rainfall time series with more than 25% missing data per month were omitted [22]. A number of 27 stations were selected with these criterions (temporal coverage: January 1981 to June 2019). It is worth mentioning that 77%, 62%, and 42% of these stations were used in the blending process of CHIRPS during 1981–1998, 1999–2013, and 2014–2019, respectively (see https://bit.ly/2ZZFAvA); therefore, this sample is not a completely independent data set [13]. As depicted in **Figure 1**,

CHIRPS rainfall estimates were obtained from the UCSB-Climate Hazards Group (CHG) webpage (https://www.chc.ucsb.edu/data; version 2 released in February 2015) at a daily time scale and spatial resolution of 0.05°, starting 1 January 1981 to 30 June 2019. This rainfall product uses a three-step development process. First, infrared precipitation (IRP) pentad (5-day) rainfall estimates are created from satellite data using cold cloud durations (CCD) lower than 235 K as a threshold value and calibrated in relation to the TRMM 3B42-based precipitation pentads by local regression. Then, the IRP pentads are divided by its long-term IRP mean values to present a percent of normal. Second, the percent of normal IRP pentad is multiplied by the corresponding Climate Hazards Precipitation

*Geographical location of the study area showing (a) selected stations. The numbers indicate the World Meteorological Organization (WMO) serial of each station; (b) annual mean precipitation for selected stations*

most stations are located in the northwest NEB or near the coast.

distribution of rainfall regimes [6, 15].

**2.2 Rainfall data sets**

**Figure 1.**

**123**

*from 1 January 1981 to 30 June 2019.*

In NEB, despite the efforts of the state climate agencies (e.g., National Center for Monitoring and Early Warning of Natural Disasters, CEMADEN; National Institute of Meteorology, INMET; Meteorology and Hydrologic Resources Foundation of Ceara, FUNCEME; Superintendence for the Development of the Northeast, SUDENE; and National Water Agency, ANA), most of the rain gauge networks currently available are inadequate to produce reliable rainfall analysis, because of their scarce spatial coverage, high proportion of missing data, and short-length records [15]. To overcome these limitations, there is a wide variety of satellite-based rainfall products, such as the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS).

CHIRPS is a quasi-global rainfall data set with relatively high spatial resolution (°0.05 °0.05) and long-term temporal coverage (from 1981 to near real time), whose processing chain blends satellite and gauge rainfall estimates [16]. Since early 2014, CHIRPS rainfall estimations are disseminated with different temporal scales (monthly, 10-day, 5-day, and daily time steps) by the University of California at Santa Barbara (UCSB). It has been subjected to various assessments worldwide by comparing to gauge measurements. According to these studies, the CHIRPS rainfall data set performs relatively well at both a regional and global scale, mainly in terms of bias and the Pearson's correlation coefficient when compared to other state-ofthe-art satellite rainfall products [1, 8, 17–21].

Unlike other natural regions, very few studies have been carried out to validate CHIRPS rainfall estimates in NEB. Overall, CHIRPS achieves better results during the rainy season (i.e., March to May), but its ability for the rain detection is poor [22]. Moreover, CHIRPS displays a rainfall pattern similar to the rain gauge data in the south-southeast subregion of the NEB, even though some performance scores are lower than the ones derived from the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) 3B42V7 product, particularly from 2012 to 2014 [23]. Interestingly, CHIRPS provides performance better in terms of rain amount than the Multi-Source Weighted-Ensemble Precipitation (MSWEP), SM2RAIN-CCI (Climate Change Initiative), and Climate Prediction Center Morphing Technique (CMORPH) rainfall products over the Cerrado biome of NEB [24]. These findings are promising for operational applications in NEB (e.g., remote drought monitoring). Nevertheless, to our knowledge, a study investigating the performance of the CHIRPS rainfall data set by using new available groundbased observations is still absent.

The purpose of this study is to evaluate the quality of the CHIRPS rainfall estimates in NEB by considering the newest in situ data from the INMET meteorological stations, which is used as a benchmark rainfall data set over a 39-year period (1981–2019).

#### **2. Materials and methods**

#### **2.1 Study area**

The study was carried out in NEB (8,515,759 km<sup>2</sup> ), which is located between 5.2° N–33.7° S and 34.7°–48.7° W [25]. In this region, the annual precipitation decreases from the east and northeast coast (>1500 mm/year) to inland dry regions (<500 mm/year) [22], due to the impact of the orography [26] and the influence of different meteorological systems, such as the intertropical convergence zone (ITCZ), squall lines (SL), easterly wave disturbances (EWD), upper tropospheric cyclonic vortices (UTCV), frontal systems (FS), mesoscale convective complexes (MCC), and the South Atlantic convergence zone (SACZ) [27]. The rainy season occurs at different times of the year: April to June in the eastern coast of the NEB; November to January in the southern part of the NEB; and March to May in the semiarid northwestern part of the NEB [27]. This region includes two main river basins, namely, the basins of the São Francisco River (where the Sobradinho reservoir is located) and the Parnaíba River. It also contains the Amazonia, Cerrado, Atlantic Forest, and Caatinga biomes, which are strongly related to the spatial distribution of rainfall regimes [6, 15].

#### **2.2 Rainfall data sets**

distortion [11]. Satellites can be used for sensing large regions with a high temporal and spatial resolution, though satellite retrieval approaches are prone to biases and systematic errors [12]. Consequently, satellite-based rainfall estimates must be validated against rain gauge data in order to assess their uncertainties before being

In NEB, despite the efforts of the state climate agencies (e.g., National Center for Monitoring and Early Warning of Natural Disasters, CEMADEN; National Institute of Meteorology, INMET; Meteorology and Hydrologic Resources Foundation of Ceara, FUNCEME; Superintendence for the Development of the Northeast, SUDENE; and National Water Agency, ANA), most of the rain gauge networks currently available are inadequate to produce reliable rainfall analysis, because of their scarce spatial coverage, high proportion of missing data, and short-length records [15]. To overcome these limitations, there is a wide variety of satellite-based rainfall products, such as the Climate Hazards Group InfraRed Precipitation with

CHIRPS is a quasi-global rainfall data set with relatively high spatial resolution (°0.05 °0.05) and long-term temporal coverage (from 1981 to near real time), whose processing chain blends satellite and gauge rainfall estimates [16]. Since early 2014, CHIRPS rainfall estimations are disseminated with different temporal scales (monthly, 10-day, 5-day, and daily time steps) by the University of California at Santa Barbara (UCSB). It has been subjected to various assessments worldwide by comparing to gauge measurements. According to these studies, the CHIRPS rainfall data set performs relatively well at both a regional and global scale, mainly in terms of bias and the Pearson's correlation coefficient when compared to other state-of-

Unlike other natural regions, very few studies have been carried out to validate CHIRPS rainfall estimates in NEB. Overall, CHIRPS achieves better results during the rainy season (i.e., March to May), but its ability for the rain detection is poor [22]. Moreover, CHIRPS displays a rainfall pattern similar to the rain gauge data in the south-southeast subregion of the NEB, even though some performance scores are lower than the ones derived from the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) 3B42V7 product, particularly from 2012 to 2014 [23]. Interestingly, CHIRPS provides performance better in terms of rain amount than the Multi-Source Weighted-Ensemble Precipitation (MSWEP), SM2RAIN-CCI (Climate Change Initiative), and Climate Prediction Center Morphing Technique (CMORPH) rainfall products over the Cerrado biome of NEB [24]. These findings are promising for operational applications in NEB (e.g., remote drought monitoring). Nevertheless, to our knowledge, a study investigating the performance of the CHIRPS rainfall data set by using new available ground-

The purpose of this study is to evaluate the quality of the CHIRPS rainfall estimates in NEB by considering the newest in situ data from the INMET meteorological stations, which is used as a benchmark rainfall data set over a 39-year period

5.2° N–33.7° S and 34.7°–48.7° W [25]. In this region, the annual precipitation decreases from the east and northeast coast (>1500 mm/year) to inland dry regions

), which is located between

used [13, 14].

*Inland Waters - Dynamics and Ecology*

Stations (CHIRPS).

the-art satellite rainfall products [1, 8, 17–21].

based observations is still absent.

**2. Materials and methods**

The study was carried out in NEB (8,515,759 km<sup>2</sup>

(1981–2019).

**2.1 Study area**

**122**

Daily rain gauge observations from rain gauge stations were provided by the INMET (www.inmet.gov.br). The higher values than daily mean 3.5 standard deviations (method for detection of outliers) were coded as missing data [20]. The daily rainfall time series with more than 25% missing data per month were omitted [22]. A number of 27 stations were selected with these criterions (temporal coverage: January 1981 to June 2019). It is worth mentioning that 77%, 62%, and 42% of these stations were used in the blending process of CHIRPS during 1981–1998, 1999–2013, and 2014–2019, respectively (see https://bit.ly/2ZZFAvA); therefore, this sample is not a completely independent data set [13]. As depicted in **Figure 1**, most stations are located in the northwest NEB or near the coast.

CHIRPS rainfall estimates were obtained from the UCSB-Climate Hazards Group (CHG) webpage (https://www.chc.ucsb.edu/data; version 2 released in February 2015) at a daily time scale and spatial resolution of 0.05°, starting 1 January 1981 to 30 June 2019. This rainfall product uses a three-step development process. First, infrared precipitation (IRP) pentad (5-day) rainfall estimates are created from satellite data using cold cloud durations (CCD) lower than 235 K as a threshold value and calibrated in relation to the TRMM 3B42-based precipitation pentads by local regression. Then, the IRP pentads are divided by its long-term IRP mean values to present a percent of normal. Second, the percent of normal IRP pentad is multiplied by the corresponding Climate Hazards Precipitation

#### **Figure 1.**

*Geographical location of the study area showing (a) selected stations. The numbers indicate the World Meteorological Organization (WMO) serial of each station; (b) annual mean precipitation for selected stations from 1 January 1981 to 30 June 2019.*

Climatology (CHPclim) pentad to generate an unbiased rainfall estimate, with units of millimeters per pentad, called the CHG IR Precipitation (CHIRP). Third, pentadal CHIRP values are disaggregated to daily precipitation estimates based on daily NOAA Climate Forecast System (CFS) fields rescaled to 0.05° resolution. Finally, CHIRPS is produced through blending stations with the CHIRP data sets via a modified inverse distance-weighted algorithm [8]. For more details about the CHIRPS data set, the reader is referred to Funk et al. [16].

the NN method instead of gridded ground-based rainfall data (e.g., via spatial interpolation) is related to the fact that the latter would involve large uncertainties given the lack of a high-density rain gauge network to reproduce adequately the rainfall gradients in NEB [22]. Secondly, an intercomparison of both rainfall data sets was carried out in order to explore the performance of the CHIRPS product at the monthly, seasonal, and annual time scales during the common temporal coverage. Consequently, several metrics on a pixel-to-station basis were computed. The Pearson's correlation coefficient (R), unbiased root mean square error (ubRMSE), and percentage bias (PBIAS) were used as continuous scores. R measures the linear relationship strength between estimations and observations, while ubRMSE and B scores measure how the value of estimates differs from the observed values [20]. To examine the rain detection capability of the CHIRPS product, the probability of detection (POD), false alarm ratio (FAR), and threat score (TS) were used as categorical scores. POD and FAR indicate the fraction of the observed events that were correctly forecasted and the fraction of the predicted events did not occur, respectively. TS is the fraction between hits to all CHIRPS-based events. The categorical scores were derived from a contingency table using a rainfall threshold of 1 mm/day to discriminate between rain and no-rain event [29] (see **Table 1**). This rainfall threshold was chosen due to its previous use in semiarid regions [22, 23, 30]. Finally, in order to investigate the influence of the rainfall station spatial distribution on the performance scores, a cluster analysis based on the k-medoid algorithm was applied using the score values of all stations as cases. This unsupervised classification technique was implemented because it is not sensitive to outliers and reduces noise [31]. The equations, ranges, and optimal values of the performance

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

CHIRPS ≥ threshold A B CHIRPS < threshold C D

*misses; D, number of correct negatives; threshold, rainfall threshold (1 mm/day).*

*Contingency table to estimate categorical scores. A, number of hits; B, number of false alarms; C, number of*

**Name Formula Range Perfect score**

*Formulas of continuous and categorical scores. G, gauge-based rainfall measurement (mm/day); S, CHIRPSbased rainfall estimate (mm/day); G* and *S, average for G and S, respectively (mm/day); N, number of data*

<sup>P</sup>ð Þ *<sup>G</sup>*�*<sup>G</sup>* ð Þ *<sup>S</sup>*�*<sup>S</sup>* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>P</sup>ð Þ *<sup>G</sup>*�*<sup>G</sup>* <sup>2</sup> q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>P</sup>ð Þ *<sup>S</sup>*�*<sup>S</sup>* <sup>2</sup> q

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 *<sup>N</sup>* ð Þ *<sup>S</sup>* � *<sup>G</sup>* <sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *RMSE*<sup>2</sup> � ð Þ *<sup>B</sup>=*<sup>100</sup> <sup>2</sup>

Pð Þ *<sup>S</sup>*�*<sup>G</sup> N*

**Gauge** ≥ **threshold Gauge < threshold**

[�1, 1] 1

(�∞, ∞) 0

q [0, ∞) 0

q [0, ∞) 0

*<sup>A</sup>*þ*<sup>C</sup>* [0, 1] <sup>1</sup>

*<sup>A</sup>*þ*<sup>B</sup>* [0, 1] <sup>0</sup>

*<sup>A</sup>*þ*B*þ*<sup>C</sup>* [0, 1] <sup>1</sup>

scores are outlined in **Table 2**.

Pearson's correlation coefficient *<sup>R</sup>* <sup>¼</sup>

Root mean square error *RMSE* <sup>¼</sup>

Unbiased root mean square error *ubRMSE* <sup>¼</sup>

Percentage bias *<sup>B</sup>* <sup>¼</sup> <sup>100</sup>

Probability of detection *POD* <sup>¼</sup> *<sup>A</sup>*

False alarm ratio *FAR* <sup>¼</sup> *<sup>B</sup>*

Threat score *TS* <sup>¼</sup> *<sup>A</sup>*

*pairs; A, B, and C for POD, FAR, and TS, as per Table 1.*

**Table 1.**

**Table 2.**

**125**

#### **2.3 Auxiliary data sets**

The land cover, annual rainfall, elevation, and type of climate were used as auxiliary information. The land cover was derived from the Land Cover-Climate Change Initiative (LC-CCI) product [28] (available online at http://maps.elie.ucl.ac. be). The average annual rainfall was estimated from the selected stations. The gauge elevation was obtained from the metadata information at each station. The slope and aspect of the terrain were derived from the Shuttle Radar Topographic Mission (SRTM) (available online at https://earthexplorer.usgs.gov). The type of climate was extracted from the Köppen-Geiger climate classification developed by Beck et al. [29] (available online at https://bit.ly/2Zt90Bu).

#### **2.4 Methodology**

The methodology applied in this study is summarized in **Figure 2**. The CHIRPS rainfall data set was chosen because of its low latency (about 3 weeks), high spatial resolution (0.05° 0.05°), daily temporal resolution, and long-term temporal coverage (1981 to near real time), respectively, so it is potentially suitable for operational purposes in NEB. Firstly, the CHIRPS product was clipped using a shapefile of NEB as a mask. Then, CHIRPS rainfall estimates were extracted using the nearest neighbor (NN) method to generate a paired rainfall data from 1 January 1981 to 30 June 2019 (i.e., the common temporal coverage). The rationale behind the choice of

**Figure 2.** *Simplified flowchart of the methodology used in this study.*

#### *Assessment of the CHIRPS-Based Satellite Precipitation Estimates DOI: http://dx.doi.org/10.5772/intechopen.91472*

the NN method instead of gridded ground-based rainfall data (e.g., via spatial interpolation) is related to the fact that the latter would involve large uncertainties given the lack of a high-density rain gauge network to reproduce adequately the rainfall gradients in NEB [22]. Secondly, an intercomparison of both rainfall data sets was carried out in order to explore the performance of the CHIRPS product at the monthly, seasonal, and annual time scales during the common temporal coverage. Consequently, several metrics on a pixel-to-station basis were computed. The Pearson's correlation coefficient (R), unbiased root mean square error (ubRMSE), and percentage bias (PBIAS) were used as continuous scores. R measures the linear relationship strength between estimations and observations, while ubRMSE and B scores measure how the value of estimates differs from the observed values [20]. To examine the rain detection capability of the CHIRPS product, the probability of detection (POD), false alarm ratio (FAR), and threat score (TS) were used as categorical scores. POD and FAR indicate the fraction of the observed events that were correctly forecasted and the fraction of the predicted events did not occur, respectively. TS is the fraction between hits to all CHIRPS-based events. The categorical scores were derived from a contingency table using a rainfall threshold of 1 mm/day to discriminate between rain and no-rain event [29] (see **Table 1**). This rainfall threshold was chosen due to its previous use in semiarid regions [22, 23, 30]. Finally, in order to investigate the influence of the rainfall station spatial distribution on the performance scores, a cluster analysis based on the k-medoid algorithm was applied using the score values of all stations as cases. This unsupervised classification technique was implemented because it is not sensitive to outliers and reduces noise [31]. The equations, ranges, and optimal values of the performance scores are outlined in **Table 2**.


#### **Table 1.**

Climatology (CHPclim) pentad to generate an unbiased rainfall estimate, with units

The land cover, annual rainfall, elevation, and type of climate were used as auxiliary information. The land cover was derived from the Land Cover-Climate Change Initiative (LC-CCI) product [28] (available online at http://maps.elie.ucl.ac. be). The average annual rainfall was estimated from the selected stations. The gauge elevation was obtained from the metadata information at each station. The slope and aspect of the terrain were derived from the Shuttle Radar Topographic Mission (SRTM) (available online at https://earthexplorer.usgs.gov). The type of climate was extracted from the Köppen-Geiger climate classification developed by Beck

The methodology applied in this study is summarized in **Figure 2**. The CHIRPS rainfall data set was chosen because of its low latency (about 3 weeks), high spatial resolution (0.05° 0.05°), daily temporal resolution, and long-term temporal coverage (1981 to near real time), respectively, so it is potentially suitable for operational purposes in NEB. Firstly, the CHIRPS product was clipped using a shapefile of NEB as a mask. Then, CHIRPS rainfall estimates were extracted using the nearest neighbor (NN) method to generate a paired rainfall data from 1 January 1981 to 30 June 2019 (i.e., the common temporal coverage). The rationale behind the choice of

of millimeters per pentad, called the CHG IR Precipitation (CHIRP). Third, pentadal CHIRP values are disaggregated to daily precipitation estimates based on daily NOAA Climate Forecast System (CFS) fields rescaled to 0.05° resolution. Finally, CHIRPS is produced through blending stations with the CHIRP data sets via a modified inverse distance-weighted algorithm [8]. For more details about the

CHIRPS data set, the reader is referred to Funk et al. [16].

et al. [29] (available online at https://bit.ly/2Zt90Bu).

**2.3 Auxiliary data sets**

*Inland Waters - Dynamics and Ecology*

**2.4 Methodology**

**Figure 2.**

**124**

*Simplified flowchart of the methodology used in this study.*

*Contingency table to estimate categorical scores. A, number of hits; B, number of false alarms; C, number of misses; D, number of correct negatives; threshold, rainfall threshold (1 mm/day).*


#### **Table 2.**

*Formulas of continuous and categorical scores. G, gauge-based rainfall measurement (mm/day); S, CHIRPSbased rainfall estimate (mm/day); G* and *S, average for G and S, respectively (mm/day); N, number of data pairs; A, B, and C for POD, FAR, and TS, as per Table 1.*

#### **3. Results**

For clarity, this section is split into three parts: (1) evaluation on annual and seasonal scales; (2) monthly variation of scores; and (3) clustering-based spatial performance.

**3.1 Evaluation on annual and seasonal scales**

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

**Figure 4.**

**127**

*value of each score is reported.*

**Figure 3** shows the spatial distribution of the continuous scores obtained after

the pixel-to-station comparison of the CHIRPS rainfall estimates against the gauge-based data set during the study period. The seasons were defined as summer

(Dec-Jan-Feb), autumn (Mar-Apr-May), winter (Jun-Jul-Aug), and spring

*Spatial distribution of POD, FAR, and TS derived from the CHIRPS rainfall estimates against ground observations for (a–c) annual; (d–f) summer; (g–i) autumn; (j–l) winter; and (m–o) spring. The median*

#### **Figure 3.**

*Spatial distribution of R, ubRMSE, and PBIAS derived from the CHIRPS rainfall estimates against ground observations for (a–c) annual; (d–f) summer; (g–i) autumn; (j–l) winter; and (m–o) spring. The median value of each score is reported.*

#### **3.1 Evaluation on annual and seasonal scales**

**3. Results**

*Inland Waters - Dynamics and Ecology*

performance.

**Figure 3.**

**126**

*value of each score is reported.*

For clarity, this section is split into three parts: (1) evaluation on annual and seasonal scales; (2) monthly variation of scores; and (3) clustering-based spatial

*Spatial distribution of R, ubRMSE, and PBIAS derived from the CHIRPS rainfall estimates against ground observations for (a–c) annual; (d–f) summer; (g–i) autumn; (j–l) winter; and (m–o) spring. The median*

**Figure 3** shows the spatial distribution of the continuous scores obtained after the pixel-to-station comparison of the CHIRPS rainfall estimates against the gauge-based data set during the study period. The seasons were defined as summer (Dec-Jan-Feb), autumn (Mar-Apr-May), winter (Jun-Jul-Aug), and spring

#### **Figure 4.**

*Spatial distribution of POD, FAR, and TS derived from the CHIRPS rainfall estimates against ground observations for (a–c) annual; (d–f) summer; (g–i) autumn; (j–l) winter; and (m–o) spring. The median value of each score is reported.*

(Sep-Oct-Nov) because the NEB is located in the southern hemisphere. The R, ubRMSE, and PBIAS median values listed in each subpanel were obtained by averaging these values from all stations via median to minimize the effects of extreme values. The CHIRPS product showed relatively good agreement with observations in terms of R, ubRMSE, and PBIAS at annual time scale (R median: 0.49; ubRMSE median: 9.73 mm/day; PBIAS, �4.10%), particularly in the northwest NEB (R > 0.50, ubRMSE and PBIAS near zero). Interestingly, the R median value begins to decrease from above 0.46 in summer to 0.32 in winter, but it rebounds and increases to values above 0.39 in spring. The ubRMSE values showed a similar pattern, with the higher ubRMSE values in summer and autumn (ubRMSE > 10 mm/day) and lower values in winter and spring (ubRMSE < 6 mm/day). The comparison revealed also that CHIRPS tends to underestimate the amount of rainfall in the course of a year (PBIAS annual median: �4.10%), especially during the transition from summer to winter (PBIAS median from �0.20% to �15.00%).

in summer and autumn (POD median > 0.50; TS median > 0.30), while lower values were observed in winter and spring. As expected, the FAR exhibited an inverse response to POD throughout the year (i.e., FAR median > 0.55 in winter and

**Figure 5** shows the median of the scores for all stations, months, and years. The

The temporal variation of POD, FAR, and TR is shown in **Figure 5**. They varied from 0.00 to 0.86, from 0.00 to 1.00, and from 0.00 to 0.68, respectively. The highest POD and TR values were observed in February and March and the lowest in July and August. This means that CHIRPS shows better performance during the rainy season in terms of detection of rain events, which is in line with those

inferences obtained from **Figure 4**. Moreover, the lowest FAR values were observed in July and August, indicating a minimum rate of false alarms during the driest

*Clustered stations according to their continuous and categorical scores at annual time scale. A 250-m digital*

median values of R, ubRMSE, and PBIAS ranged between �0.06 and 0.66, 1.48 mm/day and 19.54 mm/day, and �44.50% and 147.80%, respectively. The lowest R values were observed in August (R median: 0.16) and the highest R values in March (R median: 0.41). According to the PBIAS time series, CHIRPS tends to underestimate (overestimate) the amount of rainfall between May and August (September and April), which is consistent with the findings from **Figure 3**. A moderate linear relationship between the monthly averaged values of PBIAS and ubRMSE was also found (R = �0.35, p-value <0.05), suggesting that PBIAS tends to increase when ubRMSE decreases. Furthermore, R, ubRMSE, and PBIAS did not exhibit a long-term trend (not shown for brevity), even though they showed high values for the coeffi-

cient of variation (i.e., 51.86%, 41.82%, and 675.49%, respectively).

spring with lower values in summer and autumn).

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

**3.2 Monthly variation of scores**

**Figure 6.**

**129**

*elevation model derived from SRTM images is shown.*

For the annual time scale, the POD, FAR, and TS mean values were 0.56, 0.44, and 0.37, respectively (**Figure 4**), indicating an acceptable rain detection ability in terms of POD, even though with a medium probability of false alarms in the central NEB. Similar to R and ubRMSE (**Figure 2**), the higher POD and TS values occurred

**Figure 5.**

*Monthly time series for (a) R (dimensionless); (b) POD (dimensionless); (c) ubRMSE (mm/day); (d) FAR (dimensionless); (e) PBIAS (%); and (f) TS (dimensionless) derived from the CHIRPS rainfall estimates against ground observations (black line) for all NEB during the period 1981–2019. The red line depicts a 12 month moving average.*

#### *Assessment of the CHIRPS-Based Satellite Precipitation Estimates DOI: http://dx.doi.org/10.5772/intechopen.91472*

in summer and autumn (POD median > 0.50; TS median > 0.30), while lower values were observed in winter and spring. As expected, the FAR exhibited an inverse response to POD throughout the year (i.e., FAR median > 0.55 in winter and spring with lower values in summer and autumn).

#### **3.2 Monthly variation of scores**

(Sep-Oct-Nov) because the NEB is located in the southern hemisphere. The R, ubRMSE, and PBIAS median values listed in each subpanel were obtained by averaging these values from all stations via median to minimize the effects of extreme values. The CHIRPS product showed relatively good agreement with observations in terms of R, ubRMSE, and PBIAS at annual time scale (R median: 0.49; ubRMSE

*Inland Waters - Dynamics and Ecology*

median: 9.73 mm/day; PBIAS, �4.10%), particularly in the northwest NEB

**Figure 5.**

**128**

*month moving average.*

(R > 0.50, ubRMSE and PBIAS near zero). Interestingly, the R median value begins to decrease from above 0.46 in summer to 0.32 in winter, but it rebounds and increases to values above 0.39 in spring. The ubRMSE values showed a similar pattern, with the higher ubRMSE values in summer and autumn (ubRMSE > 10 mm/day) and lower values in winter and spring (ubRMSE < 6 mm/day). The comparison revealed also that CHIRPS tends to underestimate the amount of rainfall in the course of a year (PBIAS annual median: �4.10%), especially during the transition from summer to winter (PBIAS median from �0.20% to �15.00%). For the annual time scale, the POD, FAR, and TS mean values were 0.56, 0.44, and 0.37, respectively (**Figure 4**), indicating an acceptable rain detection ability in terms of POD, even though with a medium probability of false alarms in the central NEB. Similar to R and ubRMSE (**Figure 2**), the higher POD and TS values occurred

*Monthly time series for (a) R (dimensionless); (b) POD (dimensionless); (c) ubRMSE (mm/day); (d) FAR (dimensionless); (e) PBIAS (%); and (f) TS (dimensionless) derived from the CHIRPS rainfall estimates against ground observations (black line) for all NEB during the period 1981–2019. The red line depicts a 12-*

**Figure 5** shows the median of the scores for all stations, months, and years. The median values of R, ubRMSE, and PBIAS ranged between �0.06 and 0.66, 1.48 mm/day and 19.54 mm/day, and �44.50% and 147.80%, respectively. The lowest R values were observed in August (R median: 0.16) and the highest R values in March (R median: 0.41). According to the PBIAS time series, CHIRPS tends to underestimate (overestimate) the amount of rainfall between May and August (September and April), which is consistent with the findings from **Figure 3**. A moderate linear relationship between the monthly averaged values of PBIAS and ubRMSE was also found (R = �0.35, p-value <0.05), suggesting that PBIAS tends to increase when ubRMSE decreases. Furthermore, R, ubRMSE, and PBIAS did not exhibit a long-term trend (not shown for brevity), even though they showed high values for the coefficient of variation (i.e., 51.86%, 41.82%, and 675.49%, respectively).

The temporal variation of POD, FAR, and TR is shown in **Figure 5**. They varied from 0.00 to 0.86, from 0.00 to 1.00, and from 0.00 to 0.68, respectively. The highest POD and TR values were observed in February and March and the lowest in July and August. This means that CHIRPS shows better performance during the rainy season in terms of detection of rain events, which is in line with those inferences obtained from **Figure 4**. Moreover, the lowest FAR values were observed in July and August, indicating a minimum rate of false alarms during the driest

**Figure 6.**

*Clustered stations according to their continuous and categorical scores at annual time scale. A 250-m digital elevation model derived from SRTM images is shown.*

months. Similar to the continuous scores, these scores did not exhibit a long-term trend but a high temporal variation (i.e., 64.69%, 42.13%, and 63.97% for POD, FAR, and TR, respectively).

entire NEB (i.e., CHIRPS estimates to occur a rainfall event, but did not occur), which is also evident in **Figure 4**. It is interesting to note that the C2 stations were

A more detailed comparison, considering the auxiliary data sets (see Section 2.3), showed that there were no significant differences between both clusters in terms of average annual precipitation and terrain elevation (test based on

Wilcoxon's t-statistic at the 5% level was used). This means that these local factors did not affect the performance scores. However, regardless of the land cover, most of the C1 stations are located in open flatlands (i.e., terrain slope < 7%) with tropical savanna climate (i.e., Aw), which seem to be favorable surface conditions

Several performance scores were used to evaluate the CHIRPS rainfall product against gauge observations in Northeast Brazil during the period from January 1981 to June 2019. This region is characterized by large interannual rainfall variations and severe droughts [6, 15]. In line with previous studies [22–24], the CHIRPS data set captured relatively well the spatiotemporal pattern of rainfall across NEB, showing acceptable accuracies (see **Figures 3** and **4**), thanks to the blending process to merge the CHIRP data set derived from IR brightness temperature and TRMM,

CHIRPS exhibited poorer performance at daily time scale in terms of R (R median: 0.49) than that obtained with monthly time scale (R median: 0.94, reported by Paredes et al. [22]), indicating that increasing temporal aggregation leads to better agreement between CHIRPS and ground-based observations in NEB. This was expected because errors at daily scale time showed closely symmetric characteristics (see **Figure 5**); therefore, they tend to cancel each other during the temporal aggregation [32]. By contrast, this procedure did not provide a significant improvement on the performance in terms of PBIAS (PBIAS median: �4.10% and �3.58% [22] for daily and monthly time scales, respectively), likely due to its

These first results are consistent with the previous findings in other regions with similar climatic features such as South Sudan [33], where CHIRPS became more accurate in terms of R and RMSE as the duration of the integration time increased from months to years. It is important to note, however, that this characteristic is not unique to CHIRPS. Most of the satellite-based rainfall products tend to improve their general performance as the aggregation period increases owing to the effect of

Overall, CHIRPS showed the best (worst) performance with the (lowest) highest of R and POD and the (highest) lowest bias and FAR during the (driest) wettest months of the year (see **Figures 3** and **4**). This result is consistent with the findings of Paredes-Trejo et al. [24] and Nogueira et al. [23], who found that CHIRPS tends to overestimate low and underestimate high rainfall values in NEB. Likewise, it should be mentioned that the PBIAS and R values were highly sensitive to drought conditions, such as those observed from 2012 to 2015, where CHIRPS showed lower R values (about 0.20) and higher overestimation of the rainfall amount (see **Figure 5a** and **e**). The degradation of the performance under extreme droughts may be attributed to the evaporation processes of raindrops in the dry atmosphere before reaching the surface [20]. In this context, CHIRPS forecasts a rainfall event, but does not occur. According to the equations listed in **Table 2**, this phenomenon leads to higher PBIAS values and near-zero values for R, POD, and TS.

mostly concentrated near the coast.

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

for better performance of CHIRPS.

with ground-based observations [16].

cancelation of errors [34, 35].

**131**

high variability at daily time scale (about 700%).

**4. Discussion**

#### **3.3 Clustering-based spatial performance**

The previous statistical approaches provide a limited interpretation of the performance of CHIRPS, because they do not offer information about the degree of similarity among the selected stations in terms of their performance scores. Therefore, to identify the similar stations according to their scores, a medoid-based cluster analysis was applied. In order to adequately capture the spatiotemporal variability of the performance scores, an annual time scale was considered (i.e., **Figures 3a**–**c** and **4a–c**). The spatial distribution of the clustered stations is shown in **Figure 6** (N1, 18 stations; N2, 9 stations), while **Figure 7** displays the performance scores grouped by cluster.

Visual inspection of **Figure 7** reveals that the C1 stations showed the best performance in terms of R, ubRMSE, PBIAS, POD, and TS. The FAR values were similar in both clusters, indicating that CHIRPS tends to forecast false alarms in the

#### **Figure 7.**

*Boxplots for (a) R (dimensionless); (b) POD (dimensionless); (c) ubRMSE (mm/day); (d) FAR (dimensionless); (e) PBIAS (%); and (f) TS (dimensionless) at annual time scale grouped by cluster, where the thick line depicts the median, while the other horizontal lines of the box depict the maximum, upper quartile, lower quartile, and minimum. For clarity the outliers were omitted.*

entire NEB (i.e., CHIRPS estimates to occur a rainfall event, but did not occur), which is also evident in **Figure 4**. It is interesting to note that the C2 stations were mostly concentrated near the coast.

A more detailed comparison, considering the auxiliary data sets (see Section 2.3), showed that there were no significant differences between both clusters in terms of average annual precipitation and terrain elevation (test based on Wilcoxon's t-statistic at the 5% level was used). This means that these local factors did not affect the performance scores. However, regardless of the land cover, most of the C1 stations are located in open flatlands (i.e., terrain slope < 7%) with tropical savanna climate (i.e., Aw), which seem to be favorable surface conditions for better performance of CHIRPS.

#### **4. Discussion**

months. Similar to the continuous scores, these scores did not exhibit a long-term trend but a high temporal variation (i.e., 64.69%, 42.13%, and 63.97% for POD,

The previous statistical approaches provide a limited interpretation of the performance of CHIRPS, because they do not offer information about the degree of similarity among the selected stations in terms of their performance scores. Therefore, to identify the similar stations according to their scores, a medoid-based cluster analysis was applied. In order to adequately capture the spatiotemporal variability of the performance scores, an annual time scale was considered (i.e., **Figures 3a**–**c** and **4a–c**). The spatial distribution of the clustered stations is shown in **Figure 6** (N1, 18 stations; N2, 9 stations), while **Figure 7** displays the perfor-

Visual inspection of **Figure 7** reveals that the C1 stations showed the best performance in terms of R, ubRMSE, PBIAS, POD, and TS. The FAR values were similar in both clusters, indicating that CHIRPS tends to forecast false alarms in the

*Boxplots for (a) R (dimensionless); (b) POD (dimensionless); (c) ubRMSE (mm/day); (d) FAR*

*lower quartile, and minimum. For clarity the outliers were omitted.*

*(dimensionless); (e) PBIAS (%); and (f) TS (dimensionless) at annual time scale grouped by cluster, where the thick line depicts the median, while the other horizontal lines of the box depict the maximum, upper quartile,*

FAR, and TR, respectively).

*Inland Waters - Dynamics and Ecology*

mance scores grouped by cluster.

**Figure 7.**

**130**

**3.3 Clustering-based spatial performance**

Several performance scores were used to evaluate the CHIRPS rainfall product against gauge observations in Northeast Brazil during the period from January 1981 to June 2019. This region is characterized by large interannual rainfall variations and severe droughts [6, 15]. In line with previous studies [22–24], the CHIRPS data set captured relatively well the spatiotemporal pattern of rainfall across NEB, showing acceptable accuracies (see **Figures 3** and **4**), thanks to the blending process to merge the CHIRP data set derived from IR brightness temperature and TRMM, with ground-based observations [16].

CHIRPS exhibited poorer performance at daily time scale in terms of R (R median: 0.49) than that obtained with monthly time scale (R median: 0.94, reported by Paredes et al. [22]), indicating that increasing temporal aggregation leads to better agreement between CHIRPS and ground-based observations in NEB. This was expected because errors at daily scale time showed closely symmetric characteristics (see **Figure 5**); therefore, they tend to cancel each other during the temporal aggregation [32]. By contrast, this procedure did not provide a significant improvement on the performance in terms of PBIAS (PBIAS median: �4.10% and �3.58% [22] for daily and monthly time scales, respectively), likely due to its high variability at daily time scale (about 700%).

These first results are consistent with the previous findings in other regions with similar climatic features such as South Sudan [33], where CHIRPS became more accurate in terms of R and RMSE as the duration of the integration time increased from months to years. It is important to note, however, that this characteristic is not unique to CHIRPS. Most of the satellite-based rainfall products tend to improve their general performance as the aggregation period increases owing to the effect of cancelation of errors [34, 35].

Overall, CHIRPS showed the best (worst) performance with the (lowest) highest of R and POD and the (highest) lowest bias and FAR during the (driest) wettest months of the year (see **Figures 3** and **4**). This result is consistent with the findings of Paredes-Trejo et al. [24] and Nogueira et al. [23], who found that CHIRPS tends to overestimate low and underestimate high rainfall values in NEB. Likewise, it should be mentioned that the PBIAS and R values were highly sensitive to drought conditions, such as those observed from 2012 to 2015, where CHIRPS showed lower R values (about 0.20) and higher overestimation of the rainfall amount (see **Figure 5a** and **e**). The degradation of the performance under extreme droughts may be attributed to the evaporation processes of raindrops in the dry atmosphere before reaching the surface [20]. In this context, CHIRPS forecasts a rainfall event, but does not occur. According to the equations listed in **Table 2**, this phenomenon leads to higher PBIAS values and near-zero values for R, POD, and TS.

The sub-cloud evaporation plays an important role in the overestimation of rainfall occurrence over different semiarid and arid regions in the world [19, 32, 36]. Therefore, it can help to explain the poor performance of CHIRPS over the driest region of NEB (i.e., the Sertão region), especially in autumn and winter (see **Figures 3** and **4**) and during drought years induced by climate anomalies from the tropical Pacific Ocean (i.e., El Niño-Southern Oscillation) [37]. When this occurs, the air in the lower atmosphere is drier and hotter than usual conditions over the Sertão region [4]. Then, an intensification of the sub-cloud evaporation processes might be expected.

1.The CHIRPS rainfall data set exhibits better performance in inland regions

2.The accuracy of CHIRPS is better in the wettest months (i.e., summer) than in the driest months (i.e., winter) (see **Figures 3** and **4**). In general, CHIRPS

Based on the abovementioned conclusions, CHIRPS can serve as an alternative source of data for operational applications that require rainfall data, especially over the inland regions of NEB (see the C1 stations in **Figure 6**), during the wettest months of the year (see **Figures 3** and **4**), and at monthly or annual time scales taking advantage of the cancelation of errors of CHIRPS rainfall estimates as the duration of the integration increases [34]. However, future investigations are needed to adequately choose the operational applications of CHIRPS for each sub-

This work was funded by the Coordination for the Improvement of Higher Education Personnel (CAPES) and the National Council for Scientific and Technological Development (CNPq) (Grant no. 88887.091737/2014-01: Edital Pró-Alertas no 24/2014 under project Análise e Previsão dos Fenômenos Hidrometeorológicos Intensos do Leste do Nordeste Brasileiro). We acknowledge to the National Institute of Meteorology (INMET) and the University of California Santa Barbara's Climate

Hazards Group (CHG) for providing data that made this study possible.

The authors declare no conflict of interest.

with open flatlands than near the coast (see **Figures 6** and **7**).

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

underestimates (overestimates) high (low) rainfall amounts.

semiarid regions [19].

region of the NEB.

**Acknowledgements**

**Conflict of interest**

**133**

3.CHIRPS appears to be sensitive to the precipitation from the warm-top stratiform cloud systems (e.g., near to the coast), the warm-rain processes induced by orographic lifting (e.g., the mountain areas of NEB), and the subcloud evaporation processes (e.g., the Sertão region). The first and second are mainly attributed to a fixed IRP CCD threshold (i.e., 235 K) used by CHIRPS (see Section 2.2), which may be too cold for regions where the warm-rain processes are dominant [34], while the third is a usual phenomenon in

On a seasonal time scale, the reliability of the CHIRPS product was evident in reproducing the seasonal rainfall pattern with results comparable with the ones previously published by Melo et al. [30] for the TRMM 3B42V7 rainfall product, which is its parent rainfall product [16] (see Section 2.2). Similar to TRMM, it was found that CHIRPS exhibits poorer performance over those stations near the coast than the ones located in inland regions of NEB (see **Figures 6** and **7**), particularly in winter (see **Figures 3** and **4**). The reason behind this can be attributed to the prevalence of warm-top stratiform cloud systems along the coastal region [38, 39]. Under these conditions, CHIRPS may not detect rainfall because the cloud tops tend to have a value warmer than the IRP CCD threshold value (i.e., 235 K) [19], leading to a large underestimation in the daily precipitation and poor detection of rainfall events.

As can be seen from **Figure 6**, the landscape at most of the stations is characterized by high topographic complexity, where warm-rain processes induced by orographic lifting are dominant [40, 41]. Similar to the warm-top stratiform cloud systems in the coastal areas mentioned above, CHIRPS has limitations in reproducing the orographic rainfall due to the adoption of a fixed IRP CCD threshold value (i.e., 235 K), leading to classify warm orographic clouds as nonprecipitating [19]. Even though orographic clouds are relatively warm, they can produce substantial amounts of rain [15].

Interestingly, although the number of stations used in the CHIRPS blending process as anchor stations showed a gradual temporal decrease in NEB during the period January 1981 until June 2019 (see https://bit.ly/2ZZFAvA), there was no statistically significant trend in their performance scores (see **Figure 5**). For this study, at least 12, 19, and 21 rain gauges not included as anchor stations for the calculation of CHIRPS rainfall estimations during 1981–1998, 1999–2013, and 2014– 2019, respectively, were used. One implication of this situation is that it can be considered a relatively independent validation.

#### **5. Conclusions**

The synergetic use of ground-based rainfall observations and satellite-based rainfall estimates is of paramount importance in semiarid regions such as Northeast Brazil. CHIRPS is a state-of-the-art satellite rainfall data set characterized by its blending procedure using thermal infrared satellite observations, TRMM 3B42 based rainfall estimates, monthly precipitation climatology, and atmospheric model rainfall fields from NOAA CFS, with ground-based rainfall measurements [16]. This study set out with the aim of evaluating the performance of CHIRPS against ground-based observations in NEB. The analysis was performed on a pixel-to-station basis at daily time scale and during the period 1981–2019. The major novelty of this study with respect to previous studies [22, 23, 42] is the use of the newest in situ data from the INMET meteorological stations. The main conclusions reached are the following:


Based on the abovementioned conclusions, CHIRPS can serve as an alternative source of data for operational applications that require rainfall data, especially over the inland regions of NEB (see the C1 stations in **Figure 6**), during the wettest months of the year (see **Figures 3** and **4**), and at monthly or annual time scales taking advantage of the cancelation of errors of CHIRPS rainfall estimates as the duration of the integration increases [34]. However, future investigations are needed to adequately choose the operational applications of CHIRPS for each subregion of the NEB.

### **Acknowledgements**

The sub-cloud evaporation plays an important role in the overestimation of rainfall occurrence over different semiarid and arid regions in the world [19, 32, 36]. Therefore, it can help to explain the poor performance of CHIRPS over the driest region of NEB (i.e., the Sertão region), especially in autumn and winter (see **Figures 3** and **4**) and during drought years induced by climate anomalies from the tropical Pacific Ocean (i.e., El Niño-Southern Oscillation) [37]. When this occurs, the air in the lower atmosphere is drier and hotter than usual conditions over the Sertão region [4]. Then, an intensification of the sub-cloud evaporation processes

On a seasonal time scale, the reliability of the CHIRPS product was evident in reproducing the seasonal rainfall pattern with results comparable with the ones previously published by Melo et al. [30] for the TRMM 3B42V7 rainfall product, which is its parent rainfall product [16] (see Section 2.2). Similar to TRMM, it was found that CHIRPS exhibits poorer performance over those stations near the coast than the ones located in inland regions of NEB (see **Figures 6** and **7**), particularly in winter (see **Figures 3** and **4**). The reason behind this can be attributed to the prevalence of warm-top stratiform cloud systems along the coastal region [38, 39]. Under these conditions, CHIRPS may not detect rainfall because the cloud tops tend to have a value warmer than the IRP CCD threshold value (i.e., 235 K) [19], leading to a large underestimation in the daily precipitation and poor detection of rainfall

As can be seen from **Figure 6**, the landscape at most of the stations is characterized by high topographic complexity, where warm-rain processes induced by orographic lifting are dominant [40, 41]. Similar to the warm-top stratiform cloud systems in the coastal areas mentioned above, CHIRPS has limitations in

reproducing the orographic rainfall due to the adoption of a fixed IRP CCD threshold value (i.e., 235 K), leading to classify warm orographic clouds as nonprecipitating [19]. Even though orographic clouds are relatively warm, they can produce

Interestingly, although the number of stations used in the CHIRPS blending process as anchor stations showed a gradual temporal decrease in NEB during the period January 1981 until June 2019 (see https://bit.ly/2ZZFAvA), there was no statistically significant trend in their performance scores (see **Figure 5**). For this study, at least 12, 19, and 21 rain gauges not included as anchor stations for the calculation of CHIRPS rainfall estimations during 1981–1998, 1999–2013, and 2014– 2019, respectively, were used. One implication of this situation is that it can be

The synergetic use of ground-based rainfall observations and satellite-based rainfall estimates is of paramount importance in semiarid regions such as Northeast Brazil. CHIRPS is a state-of-the-art satellite rainfall data set characterized by its blending procedure using thermal infrared satellite observations, TRMM 3B42 based rainfall estimates, monthly precipitation climatology, and atmospheric model rainfall fields from NOAA CFS, with ground-based rainfall measurements [16]. This study set out with the aim of evaluating the performance of CHIRPS against ground-based observations in NEB. The analysis was performed on a pixel-to-station basis at daily time scale and during the period 1981–2019. The major novelty of this study with respect to previous studies [22, 23, 42] is the use of the newest in situ data from the INMET meteorological stations. The main conclusions reached are the

might be expected.

*Inland Waters - Dynamics and Ecology*

events.

substantial amounts of rain [15].

**5. Conclusions**

following:

**132**

considered a relatively independent validation.

This work was funded by the Coordination for the Improvement of Higher Education Personnel (CAPES) and the National Council for Scientific and Technological Development (CNPq) (Grant no. 88887.091737/2014-01: Edital Pró-Alertas no 24/2014 under project Análise e Previsão dos Fenômenos Hidrometeorológicos Intensos do Leste do Nordeste Brasileiro). We acknowledge to the National Institute of Meteorology (INMET) and the University of California Santa Barbara's Climate Hazards Group (CHG) for providing data that made this study possible.

#### **Conflict of interest**

The authors declare no conflict of interest.

#### **Author details**

Franklin Paredes-Trejo<sup>1</sup> , Humberto Alves Barbosa<sup>2</sup> \*, Tumuluru Venkata Lakshmi Kumar<sup>3</sup> , Manoj Kumar Thakur<sup>4</sup> and Catarina de Oliveira Buriti5

1 University of the Western Plains Ezequiel Zamora, San Carlos, Venezuela

2 Laboratory for Analyzing and Processing Satellite Images, Federal University of Alagoas, Brazil

**References**

2017

1310-1

joc.5225

**135**

jaridenv.2015.08.015

[7] Michaelides S, Levizzani V, Anagnostou E, Bauer P, Kasparis T,

[1] Beck HE, Vergopolan N, Pan M, Levizzani V, Van Dijk AIJM, Weedon GP, et al. Global-scale evaluation of 22 precipitation datasets

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

Lane JE. Precipitation: Measurement, remote sensing, climatology and

[8] Bai L, Shi C, Li L, Yang Y, Wu J. Accuracy of CHIRPS satellite-rainfall products over mainland China. Remote Sensing. 2018;**10**(3):362. DOI: 10.3390/

[9] Kidd C, Becker A, Huffman GJ, Muller CL, Joe P, Skofronick-Jackson G, et al. So, how much of the Earth's surface is covered by rain gauges? Bulletin of the American Meteorological

Society. 2017;**98**(1):69-78. DOI: 10.1175/BAMS-D-14-00283.1

[10] Brocca L, Filippucci P, Hahn S, Ciabatta L, Massari C, Camici S, et al. SM2RAIN–ASCAT (2007–2018): Global daily satellite rainfall data from ASCAT soil moisture observations. Earth System Science Data. 2019;**11**(4):1583-1601. DOI: 10.5194/essd-11-1583-2019

[11] Raghavan S. Radar Meteorology. Dordrecht: Springer; 2013. p. 549. DOI:

10.1007/978-94-017-0201-0

15-0094.1

2017RG000562

[12] Maggioni V, Sapiano MRP, Adler RF. Estimating uncertainties in high-resolution satellite precipitation products: Systematic or random error? Journal of Hydrometeorology. 2016; **17**(4):1119-1129. DOI: 10.1175/JHM-D-

[13] Loew A, Bell W, Brocca L, Bulgin CE, Burdanowitz J, Calbet X, et al. Validation practices for satellitebased Earth observation data across communities. Reviews of Geophysics. 2017;**55**(3):779-817. DOI: 10.1002/

[14] Kumar TVL, Barbosa HA,

Thakur MK, Paredes-Trejo F. Validation

**94**(4):512-533. DOI: 10.1016/j.

atmosres.2009.08.017

rs10030362

modeling. Atmospheric Research. 2009;

hydrological modeling. Hydrology and Earth System Sciences. 2017;**21**(12): 6201-6217. DOI: 10.5194/hess-21-6201-

[2] Zambrano F, Wardlow B, Tadesse T, Lillo-Saavedra M, Lagos O. Evaluating satellite-derived long-term historical precipitation datasets for drought monitoring in Chile. Atmospheric Research. 2017;**186**:26-42. DOI: 10.1016/

[3] Funk CC, Peterson PJ, Landsfeld MF, Pedreros DH, Verdin JP, Rowland JD, et al. A quasi-global precipitation time series for drought monitoring. US Geological Survey Data Series. 2014; **832**(4):1-12. DOI: 10.3133/ds832

[4] Marengo JA, Bernasconi M. Regional

Marengo JA, Carvalho MA. Frequency, duration and severity of drought in the Semiarid Northeast Brazil region. International Journal of Climatology. 2018;**38**(2):517-529. DOI: 10.1002/

[6] Barbosa HA, Lakshmi Kumar TV. Influence of rainfall variability on the vegetation dynamics over Northeastern Brazil. Journal of Arid Environments. 2016;**124**:377-387. DOI: 10.1016/j.

differences in aridity/drought conditions over Northeast Brazil: Present state and future projections. Climatic Change. 2015;**129**(1–2): 103-115. DOI: 10.1007/s10584-014-

[5] Brito SSB, Cunha APMA, Cunningham CC, Alvalá RC,

using gauge observations and

j.atmosres.2016.11.006

3 Atmospheric Science Research Laboratory, Department of Physics, SRM Institute of Science and Technology, Tamilnadu, India

4 Tribhuvan University, Kathmandu, Nepal

5 National Semi-Arid Institute (INSA), Ministry of Science, Technology, Innovations and Communications (MCTIC), Brazil

\*Address all correspondence to: barbosa33@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates DOI: http://dx.doi.org/10.5772/intechopen.91472*

#### **References**

[1] Beck HE, Vergopolan N, Pan M, Levizzani V, Van Dijk AIJM, Weedon GP, et al. Global-scale evaluation of 22 precipitation datasets using gauge observations and hydrological modeling. Hydrology and Earth System Sciences. 2017;**21**(12): 6201-6217. DOI: 10.5194/hess-21-6201- 2017

[2] Zambrano F, Wardlow B, Tadesse T, Lillo-Saavedra M, Lagos O. Evaluating satellite-derived long-term historical precipitation datasets for drought monitoring in Chile. Atmospheric Research. 2017;**186**:26-42. DOI: 10.1016/ j.atmosres.2016.11.006

[3] Funk CC, Peterson PJ, Landsfeld MF, Pedreros DH, Verdin JP, Rowland JD, et al. A quasi-global precipitation time series for drought monitoring. US Geological Survey Data Series. 2014; **832**(4):1-12. DOI: 10.3133/ds832

[4] Marengo JA, Bernasconi M. Regional differences in aridity/drought conditions over Northeast Brazil: Present state and future projections. Climatic Change. 2015;**129**(1–2): 103-115. DOI: 10.1007/s10584-014- 1310-1

[5] Brito SSB, Cunha APMA, Cunningham CC, Alvalá RC, Marengo JA, Carvalho MA. Frequency, duration and severity of drought in the Semiarid Northeast Brazil region. International Journal of Climatology. 2018;**38**(2):517-529. DOI: 10.1002/ joc.5225

[6] Barbosa HA, Lakshmi Kumar TV. Influence of rainfall variability on the vegetation dynamics over Northeastern Brazil. Journal of Arid Environments. 2016;**124**:377-387. DOI: 10.1016/j. jaridenv.2015.08.015

[7] Michaelides S, Levizzani V, Anagnostou E, Bauer P, Kasparis T, Lane JE. Precipitation: Measurement, remote sensing, climatology and modeling. Atmospheric Research. 2009; **94**(4):512-533. DOI: 10.1016/j. atmosres.2009.08.017

[8] Bai L, Shi C, Li L, Yang Y, Wu J. Accuracy of CHIRPS satellite-rainfall products over mainland China. Remote Sensing. 2018;**10**(3):362. DOI: 10.3390/ rs10030362

[9] Kidd C, Becker A, Huffman GJ, Muller CL, Joe P, Skofronick-Jackson G, et al. So, how much of the Earth's surface is covered by rain gauges? Bulletin of the American Meteorological Society. 2017;**98**(1):69-78. DOI: 10.1175/BAMS-D-14-00283.1

[10] Brocca L, Filippucci P, Hahn S, Ciabatta L, Massari C, Camici S, et al. SM2RAIN–ASCAT (2007–2018): Global daily satellite rainfall data from ASCAT soil moisture observations. Earth System Science Data. 2019;**11**(4):1583-1601. DOI: 10.5194/essd-11-1583-2019

[11] Raghavan S. Radar Meteorology. Dordrecht: Springer; 2013. p. 549. DOI: 10.1007/978-94-017-0201-0

[12] Maggioni V, Sapiano MRP, Adler RF. Estimating uncertainties in high-resolution satellite precipitation products: Systematic or random error? Journal of Hydrometeorology. 2016; **17**(4):1119-1129. DOI: 10.1175/JHM-D-15-0094.1

[13] Loew A, Bell W, Brocca L, Bulgin CE, Burdanowitz J, Calbet X, et al. Validation practices for satellitebased Earth observation data across communities. Reviews of Geophysics. 2017;**55**(3):779-817. DOI: 10.1002/ 2017RG000562

[14] Kumar TVL, Barbosa HA, Thakur MK, Paredes-Trejo F. Validation

**Author details**

Alagoas, Brazil

**134**

Franklin Paredes-Trejo<sup>1</sup>

Tumuluru Venkata Lakshmi Kumar<sup>3</sup>

of Science and Technology, Tamilnadu, India

4 Tribhuvan University, Kathmandu, Nepal

provided the original work is properly cited.

Innovations and Communications (MCTIC), Brazil

\*Address all correspondence to: barbosa33@gmail.com

and Catarina de Oliveira Buriti5

*Inland Waters - Dynamics and Ecology*

, Humberto Alves Barbosa<sup>2</sup>

1 University of the Western Plains Ezequiel Zamora, San Carlos, Venezuela

5 National Semi-Arid Institute (INSA), Ministry of Science, Technology,

2 Laboratory for Analyzing and Processing Satellite Images, Federal University of

3 Atmospheric Science Research Laboratory, Department of Physics, SRM Institute

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*,

, Manoj Kumar Thakur<sup>4</sup>

of satellite (TMPA and IMERG) rainfall products with the IMD gridded data sets over monsoon core region of India. In: Rustamov RB, editor. Satellite Information Classification and Interpretation. Rijeka: IntechOpen; 2019. p. 13. DOI: 10.5772/ intechopen.77202

[15] Correia Filho WLF, De Oliveira-Júnior JF, De Barros SD, De Bodas Terassi PM, Teodoro PE, De Gois G, et al. Rainfall variability in the Brazilian northeast biomes and their interactions with meteorological systems and ENSO via CHELSA product. Big Earth Data. 2019;**3**(4):315-337. DOI: 10.1080/ 20964471.2019.1692298

[16] Funk C, Peterson P, Landsfeld M, Pedreros D, Verdin J, Shukla S, et al. The climate hazards infrared precipitation with stations—A new environmental record for monitoring extremes. Scientific Data. 2015;**2**: 150066. DOI: 10.1038/sdata.2015.66

[17] Paredes Trejo FJ, Barbosa HA, Peñaloza-Murillo MA, Alejandra Moreno M, Farías A. Intercomparison of improved satellite rainfall estimation with CHIRPS gridded product and rain gauge data over Venezuela. Atmosfera. 2016;**29**(4):323-342. DOI: 10.20937/ ATM.2016.29.04.04

[18] Prakash S. Performance assessment of CHIRPS, MSWEP, SM2RAIN-CCI, and TMPA precipitation products across India. Journal of Hydrology. 2019;**571**: 50-59. DOI: 10.1016/j.jhydrol.2019. 01.036

[19] Dinku T, Funk C, Peterson P, Maidment R, Tadesse T, Gadain H, et al. Validation of the CHIRPS satellite rainfall estimates over Eastern Africa. Quarterly Journal of the Royal Meteorological Society. 2018;**144**(S1): 292-312. DOI: 10.1002/qj.3244

[20] Rivera JA, Marianetti G, Hinrichs S. Validation of CHIRPS precipitation

dataset along the Central Andes of Argentina. Atmospheric Research. 2018; **213**:437-449. DOI: 10.1016/j.atmosres. 2018.06.023

[28] Houghton RA, Bontemps S, Peng S, Lamarche C, Li W, MacBean N, et al. Gross and net land cover changes based on plant functional types derived from the annual ESA CCI land cover maps. Earth System Science Data Discussions. 2017;**10**(1):1-23. DOI: 10.5194/essd-

*DOI: http://dx.doi.org/10.5772/intechopen.91472*

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates*

Sensing. 2019;**11**(22):1-22. DOI:

[35] Dembélé M, Zwart SJ. Evaluation and comparison of satellite-based rainfall products in Burkina Faso, West Africa. International Journal of Remote Sensing. 2016;**37**(17):3995-4014. DOI: 10.1080/01431161.2016.1207258

[36] Saeidizand R, Sabetghadam S, Tarnavsky E, Pierleoni A. Evaluation of CHIRPS rainfall estimates over Iran. Quarterly Journal of the Royal Meteorological Society. 2018;**144**: 282-291. DOI: 10.1002/qj.3342

[37] Marengo JA, Torres RR, Alves LM. Drought in Northeast Brazil—Past, present, and future. Theoretical and Applied Climatology. 2017;**129**(3–4): 1189-1200. DOI: 10.1007/s00704-016-

[38] Rozante J, Vila D, Barboza Chiquetto J, Fernandes A, Souza AD. Evaluation of TRMM/GPM blended daily products over Brazil. Remote Sensing. 2018;**10**(6):882. DOI: 10.3390/

[39] Fedorova N, Levit V, Fedorov D. Fog and stratus formation on the coast of Brazil. Atmospheric Research. 2008; **87**(3–4):268-278. DOI: 10.1016/j.

Altitudinal precipitation gradients in the

10.3390/rs11222688

1840-8

rs10060882

14-0178.1

2008JHM973.1

atmosres.2007.11.008

[40] Anders AM, Nesbitt SW.

tropics from Tropical Rainfall Measuring Mission (TRMM) precipitation radar. Journal of Hydrometeorology. 2015;**16**(1): 441-448. DOI: 10.1175/JHM-D-

[41] Giovannettone JP, Barros AP. Probing regional orographic controls of precipitation and cloudiness in the central Andes using satellite data. Journal of Hydrometeorology. 2009;

**10**(1):167-182. DOI: 10.1175/

[29] Beck HE, Zimmermann NE, McVicar TR, Vergopolan N, Berg A, Wood EF. Present and future Köppen-Geiger climate classification maps at 1 km resolution. Scientific Data. 2018;**5**: 180214. DOI: 10.1038/sdata.2018.214

10.1002/2015JD023797

procs.2016.02.095

amt-2017-294

**137**

[30] Melo D d CD, Xavier AC, Bianchi T, Oliveira PTS, Scanlon BR, Lucas MC, et al. Performance evaluation of rainfall estimates by TRMM multi-satellite precipitation analysis 3B42V6 and V7 over Brazil. Journal of Geophysical Research. 2015;**120**(18):9426-9436. DOI:

[31] Arora P, Varshney S, et al. Analysis of k-means and k-medoids algorithm for big data. Procedia Computer Science. 2016;**78**:507-512. DOI: 10.1016/j.

[32] Ayehu GT, Tadesse T, Gessesse B, Dinku T. Validation of new satellite rainfall products over the Upper Blue Nile Basin, Ethiopia. Atmospheric Measurement Techniques Discussions. 2017;**11**(November):1-24. DOI: 10.5194/

[33] Basheer M, Elagib NA. Performance of satellite-based and GPCC 7.0 rainfall products in an extremely data-scarce country in the Nile Basin. Atmospheric Research. 2019;**215**:128-140. DOI: 10.1016/j.atmosres.2018.08.028

[34] Belay AS, Fenta AA, Yenehun A, Nigate F, Tilahun SA, Moges MM, et al. Evaluation and application of multisource satellite rainfall product CHIRPS to assess spatio-temporal rainfall variability on data-sparse western margins of Ethiopian highlands. Remote

2017-74

[21] Zambrano-Bigiarini M, Nauditt A, Birkel C, Verbist K, Ribbe L. Temporal and spatial evaluation of satellite-based rainfall estimates across the complex topographical and climatic gradients of Chile. Hydrology and Earth System Sciences. 2017;**21**:1295-1320. DOI: 10.5194/hess-21-1295-2017

[22] Paredes F, Barbosa HA, Lakshmi-Kumar T. Validating CHIRPS-based satellite precipitation estimates in Northeast Brazil. Journal of Arid Environments. 2016;**139**:26-40. DOI: 10.1016/j.jaridenv.2016.12.009

[23] Nogueira SMC, Moreira MA, Volpato MML. Evaluating precipitation estimates from Eta, TRMM and CHRIPS data in the south-southeast region of Minas Gerais state-Brazil. Remote Sensing. 2018;**10**(2):313. DOI: 10.3390/ rs10020313

[24] Paredes-Trejo F, Barbosa H, Rossato L. Assessment of SM2RAINderived and state-of-the-art satellite rainfall products over Northeastern Brazil. Remote Sensing. 2018;**10**(7): 1093. DOI: 10.3390/rs10071093

[25] Instituto Brasileiro de Geografia e Estatística. 2010 Census (Censo 2010). [Online] IBGE. Available from: https:// bit.ly/2Nufhsu [Accessed: 07 March 2019]

[26] Junquas C, Li L, Vera CS, Le Treut H, Takahashi K. Influence of South America orography on summertime precipitation in Southeastern South America. Climate Dynamics. 2016;**46**(11–12):3941-3963. DOI: 10.1007/s00382-015-2814-8

[27] Molion LCB, Bernardo S. de O. Uma revisão da dinâmica das chuvas no nordeste brasileiro. Revista Brasileira de Meteorologia. 2002;**17**(1):1-10

*Assessment of the CHIRPS-Based Satellite Precipitation Estimates DOI: http://dx.doi.org/10.5772/intechopen.91472*

[28] Houghton RA, Bontemps S, Peng S, Lamarche C, Li W, MacBean N, et al. Gross and net land cover changes based on plant functional types derived from the annual ESA CCI land cover maps. Earth System Science Data Discussions. 2017;**10**(1):1-23. DOI: 10.5194/essd-2017-74

of satellite (TMPA and IMERG) rainfall products with the IMD gridded data sets over monsoon core region of India. In:

*Inland Waters - Dynamics and Ecology*

dataset along the Central Andes of Argentina. Atmospheric Research. 2018; **213**:437-449. DOI: 10.1016/j.atmosres.

[21] Zambrano-Bigiarini M, Nauditt A, Birkel C, Verbist K, Ribbe L. Temporal and spatial evaluation of satellite-based rainfall estimates across the complex topographical and climatic gradients of Chile. Hydrology and Earth System Sciences. 2017;**21**:1295-1320. DOI: 10.5194/hess-21-1295-2017

[22] Paredes F, Barbosa HA, Lakshmi-Kumar T. Validating CHIRPS-based satellite precipitation estimates in Northeast Brazil. Journal of Arid Environments. 2016;**139**:26-40. DOI: 10.1016/j.jaridenv.2016.12.009

[23] Nogueira SMC, Moreira MA, Volpato MML. Evaluating precipitation estimates from Eta, TRMM and CHRIPS data in the south-southeast region of Minas Gerais state-Brazil. Remote Sensing. 2018;**10**(2):313. DOI: 10.3390/

[24] Paredes-Trejo F, Barbosa H, Rossato L. Assessment of SM2RAINderived and state-of-the-art satellite rainfall products over Northeastern Brazil. Remote Sensing. 2018;**10**(7): 1093. DOI: 10.3390/rs10071093

[25] Instituto Brasileiro de Geografia e Estatística. 2010 Census (Censo 2010). [Online] IBGE. Available from: https:// bit.ly/2Nufhsu [Accessed: 07 March 2019]

Le Treut H, Takahashi K. Influence of

Southeastern South America. Climate Dynamics. 2016;**46**(11–12):3941-3963. DOI: 10.1007/s00382-015-2814-8

[27] Molion LCB, Bernardo S. de O. Uma revisão da dinâmica das chuvas no nordeste brasileiro. Revista Brasileira de

Meteorologia. 2002;**17**(1):1-10

[26] Junquas C, Li L, Vera CS,

South America orography on summertime precipitation in

2018.06.023

rs10020313

Rustamov RB, editor. Satellite Information Classification and Interpretation. Rijeka: IntechOpen;

[15] Correia Filho WLF, De Oliveira-Júnior JF, De Barros SD, De Bodas Terassi PM, Teodoro PE, De Gois G, et al. Rainfall variability in the Brazilian northeast biomes and their interactions with meteorological systems and ENSO via CHELSA product. Big Earth Data. 2019;**3**(4):315-337. DOI: 10.1080/

[16] Funk C, Peterson P, Landsfeld M, Pedreros D, Verdin J, Shukla S, et al.

2019. p. 13. DOI: 10.5772/

20964471.2019.1692298

The climate hazards infrared precipitation with stations—A new environmental record for monitoring extremes. Scientific Data. 2015;**2**: 150066. DOI: 10.1038/sdata.2015.66

[17] Paredes Trejo FJ, Barbosa HA, Peñaloza-Murillo MA, Alejandra

ATM.2016.29.04.04

01.036

**136**

Moreno M, Farías A. Intercomparison of improved satellite rainfall estimation with CHIRPS gridded product and rain gauge data over Venezuela. Atmosfera. 2016;**29**(4):323-342. DOI: 10.20937/

[18] Prakash S. Performance assessment of CHIRPS, MSWEP, SM2RAIN-CCI, and TMPA precipitation products across India. Journal of Hydrology. 2019;**571**: 50-59. DOI: 10.1016/j.jhydrol.2019.

[19] Dinku T, Funk C, Peterson P, Maidment R, Tadesse T, Gadain H, et al. Validation of the CHIRPS satellite rainfall estimates over Eastern Africa.

Quarterly Journal of the Royal

292-312. DOI: 10.1002/qj.3244

Meteorological Society. 2018;**144**(S1):

[20] Rivera JA, Marianetti G, Hinrichs S. Validation of CHIRPS precipitation

intechopen.77202

[29] Beck HE, Zimmermann NE, McVicar TR, Vergopolan N, Berg A, Wood EF. Present and future Köppen-Geiger climate classification maps at 1 km resolution. Scientific Data. 2018;**5**: 180214. DOI: 10.1038/sdata.2018.214

[30] Melo D d CD, Xavier AC, Bianchi T, Oliveira PTS, Scanlon BR, Lucas MC, et al. Performance evaluation of rainfall estimates by TRMM multi-satellite precipitation analysis 3B42V6 and V7 over Brazil. Journal of Geophysical Research. 2015;**120**(18):9426-9436. DOI: 10.1002/2015JD023797

[31] Arora P, Varshney S, et al. Analysis of k-means and k-medoids algorithm for big data. Procedia Computer Science. 2016;**78**:507-512. DOI: 10.1016/j. procs.2016.02.095

[32] Ayehu GT, Tadesse T, Gessesse B, Dinku T. Validation of new satellite rainfall products over the Upper Blue Nile Basin, Ethiopia. Atmospheric Measurement Techniques Discussions. 2017;**11**(November):1-24. DOI: 10.5194/ amt-2017-294

[33] Basheer M, Elagib NA. Performance of satellite-based and GPCC 7.0 rainfall products in an extremely data-scarce country in the Nile Basin. Atmospheric Research. 2019;**215**:128-140. DOI: 10.1016/j.atmosres.2018.08.028

[34] Belay AS, Fenta AA, Yenehun A, Nigate F, Tilahun SA, Moges MM, et al. Evaluation and application of multisource satellite rainfall product CHIRPS to assess spatio-temporal rainfall variability on data-sparse western margins of Ethiopian highlands. Remote Sensing. 2019;**11**(22):1-22. DOI: 10.3390/rs11222688

[35] Dembélé M, Zwart SJ. Evaluation and comparison of satellite-based rainfall products in Burkina Faso, West Africa. International Journal of Remote Sensing. 2016;**37**(17):3995-4014. DOI: 10.1080/01431161.2016.1207258

[36] Saeidizand R, Sabetghadam S, Tarnavsky E, Pierleoni A. Evaluation of CHIRPS rainfall estimates over Iran. Quarterly Journal of the Royal Meteorological Society. 2018;**144**: 282-291. DOI: 10.1002/qj.3342

[37] Marengo JA, Torres RR, Alves LM. Drought in Northeast Brazil—Past, present, and future. Theoretical and Applied Climatology. 2017;**129**(3–4): 1189-1200. DOI: 10.1007/s00704-016- 1840-8

[38] Rozante J, Vila D, Barboza Chiquetto J, Fernandes A, Souza AD. Evaluation of TRMM/GPM blended daily products over Brazil. Remote Sensing. 2018;**10**(6):882. DOI: 10.3390/ rs10060882

[39] Fedorova N, Levit V, Fedorov D. Fog and stratus formation on the coast of Brazil. Atmospheric Research. 2008; **87**(3–4):268-278. DOI: 10.1016/j. atmosres.2007.11.008

[40] Anders AM, Nesbitt SW. Altitudinal precipitation gradients in the tropics from Tropical Rainfall Measuring Mission (TRMM) precipitation radar. Journal of Hydrometeorology. 2015;**16**(1): 441-448. DOI: 10.1175/JHM-D-14-0178.1

[41] Giovannettone JP, Barros AP. Probing regional orographic controls of precipitation and cloudiness in the central Andes using satellite data. Journal of Hydrometeorology. 2009; **10**(1):167-182. DOI: 10.1175/ 2008JHM973.1

*Inland Waters - Dynamics and Ecology*

[42] Paredes-Trejo F, Barbosa H, dos Santos CAC, Paredes-Trejo F, Barbosa H, dos Santos CAC. Evaluation of the performance of SM2RAINderived rainfall products over Brazil. Remote Sensing. 2019;**11**(9):1113. DOI: 10.3390/RS11091113

**139**

**Chapter 9**

**Abstract**

province, China.

**1. Introduction**

dual-threshold segmentation

environmental monitoring [1].

Improved Narrow Water

*Wu Bo, Zhang Jinmu and Zhao Yindi*

Extraction Using a Morphological

An improved water extraction method using a morphological linear enhancement

technique is proposed to improve the delineation of narrow water features for the modified normalized difference water index (MNDWI) derived from remote sensing images. This method introduces a morphological white top-hat (WTH) transforming operation on the MNDWI to extract multi-scale and multidirectional differential morphological profiles and constructs a morphological narrow water index (MNWI). The MNWI can effectively enhance the local contrast of linear objects, allowing narrow water bodies to be easily separated from mountain shadows and other features. Furthermore, to accurately delineate surface water bodies, a dual-threshold segmentation method was also developed by combining an empirical threshold segmentation with the MNDWI for wide water bodies and an automatic threshold segmentation with the MNWI for narrow water bodies. This method was validated using three experimental datasets, which were taken from two different Landsat images. Our results demonstrate that narrow water bodies can be sufficiently identified, with an overall accuracy of over 90%. Most narrow streams or rivers keep a continuous shape in space, and the boundaries of the water bodies are accurately delineated as compared with the MNDWI method. Finally, the proposed method was used to extract the entire inland surface water of Fujian

**Keywords:** narrow water extraction, white top-hat transform, MNWI,

Surface water is one the most vital earth resources undergoing changes in time and space as a consequence of land use/cover (LULC) changes, climate change, and other forms of environmental changes in many parts of the world. Timely and accurate monitoring and delivery of data of the dynamics of surface water are, therefore, critically important in various scientific disciplines, such as the assessment of present and future water resources, climate models, agricultural suitability, river dynamics, wetland inventory, watershed analysis, surface water surveys, and

Remote sensing at different spatial, spectral, and temporal resolutions provides an enormous amount of data for mapping water resources and its dynamics at local

Linear Enhancement Technique

#### **Chapter 9**

[42] Paredes-Trejo F, Barbosa H, dos Santos CAC, Paredes-Trejo F,

*Inland Waters - Dynamics and Ecology*

10.3390/RS11091113

**138**

Barbosa H, dos Santos CAC. Evaluation of the performance of SM2RAINderived rainfall products over Brazil. Remote Sensing. 2019;**11**(9):1113. DOI:

## Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique

*Wu Bo, Zhang Jinmu and Zhao Yindi*

#### **Abstract**

An improved water extraction method using a morphological linear enhancement technique is proposed to improve the delineation of narrow water features for the modified normalized difference water index (MNDWI) derived from remote sensing images. This method introduces a morphological white top-hat (WTH) transforming operation on the MNDWI to extract multi-scale and multidirectional differential morphological profiles and constructs a morphological narrow water index (MNWI). The MNWI can effectively enhance the local contrast of linear objects, allowing narrow water bodies to be easily separated from mountain shadows and other features. Furthermore, to accurately delineate surface water bodies, a dual-threshold segmentation method was also developed by combining an empirical threshold segmentation with the MNDWI for wide water bodies and an automatic threshold segmentation with the MNWI for narrow water bodies. This method was validated using three experimental datasets, which were taken from two different Landsat images. Our results demonstrate that narrow water bodies can be sufficiently identified, with an overall accuracy of over 90%. Most narrow streams or rivers keep a continuous shape in space, and the boundaries of the water bodies are accurately delineated as compared with the MNDWI method. Finally, the proposed method was used to extract the entire inland surface water of Fujian province, China.

**Keywords:** narrow water extraction, white top-hat transform, MNWI, dual-threshold segmentation

#### **1. Introduction**

Surface water is one the most vital earth resources undergoing changes in time and space as a consequence of land use/cover (LULC) changes, climate change, and other forms of environmental changes in many parts of the world. Timely and accurate monitoring and delivery of data of the dynamics of surface water are, therefore, critically important in various scientific disciplines, such as the assessment of present and future water resources, climate models, agricultural suitability, river dynamics, wetland inventory, watershed analysis, surface water surveys, and environmental monitoring [1].

Remote sensing at different spatial, spectral, and temporal resolutions provides an enormous amount of data for mapping water resources and its dynamics at local to global scales. At a result, it has become a routine approach for the monitoring of land surface water bodies, since the acquired data can provide macroscopic, real-time, dynamic, and cost-effective information, which is substantially different from conventional in situ measurements. Various approaches for water body extraction from multispectral images have been developed in the past decades [2–4], which can be broadly grouped into three categories: spectral band segmentation, image supervised classification, and water indices. Among all these methods, of particular interest is the spectral water index-based method, as it is a reliable and cost-effective method. This type of method takes advantage of reflectivity differences of each involved band for water body extraction based on the analysis of signature differences between water and other surfaces.

One of the most widely used indexes is the normalized difference water index (NDWI) [4], which utilizes the green (band 2) and near-infrared (band 4) of Landsat TM to delineate open water features. However, Xu found that the NDWI cannot efficiently suppress the signal from built-up surfaces and therefore proposed an improved one, called modified normalized difference water index (MNDWI) [5], where the NDWI was modified by replacing band 4 with band 5 of Landsat TM/ETM. The MNDWI has been validated as one of the most widely used water indices for various applications, though it is still difficult to obtain a high accuracy of water extraction in complex circumstances. Carleer and Wolff [6], among others, have found that the land cover classifications of water and shadow can often be confused. This issue often arises in environments where a large amount of shadow and water regions exist, such as urban and mountainous landscapes. The identification of narrow water bodies (such as narrow streams, canals, ponds, small reservoirs, etc.) can be a difficult task when using NDWI or MNDWI images, because the shallow and narrow water pixels may generate unstable spectral profiles or characteristics, due to the mixed reflectance caused by sediment and/or adjacent land covers. Narrow water is typically defined as a water body with an apparent width less than or equal to three pixels in an image. Therefore, narrow water features often contain mixed pixels, and the extraction of them from NDWI or MNDWI images generally exhibits a discontinuous shape in space.

To remedy this problem, past studies have attempted to identify narrow water features by combining different procedures. Yang et al. proposed a method of extracting initial water information via a user-defined specified water index, and then they performed a series of operations. These operations include morphological dilation, image filtering, and thinning techniques applied to the water index image to recover the continuity of narrow rivers or streams [7]. This method can be effective in the extraction of narrow water bodies if the water disruption is short; however, it may increase false water identification when water disruption is large, since it is dependent on the morphological dilation operation to reconnect the narrow rivers. Such simple threshold techniques are not often a sufficient solution to identify narrow water bodies; therefore, Li et al. suggested an object-oriented method of small water body extraction [8]. They first extracted textural and shaperelated features from images as supplementary information to spectral bands and then performed a segmentation operation on the images using an optimal scale to identify the potential water bodies. Yet, their method is not an automatic process, since it involves multiple user-defined parameters in image segmentation, which prohibits its use in large areas. An alternative approach was performed by Jiang et al. who extracted narrow water features via the enhancement of linear features in NDWI images [9]. However, their procedure involves multiple empirical thresholds, so it is not a cost-effective method for water feature extraction on large scale.

Attempting to improve on these previous approaches, here we propose an automatic water extraction method that constructs a novel narrow water index,

**141**

calculated as:

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique*

denoted as morphological narrow water index (MNWI). The MNWI is constructed using multi-scale and multidirectional differential morphological profiles (DMPs) on a MNDWI image, and then water bodies are automatically extracted using a dual-threshold segmentation. The successful use of DMPs to extract various thematic information from images has been sufficiently validated, such as buildings in urban areas [10, 11], rare earth mining areas [12], and mapping of mangrove forests [13]. In this paper, we introduce a DMP technique to highlight the contrast of bright features as a way of narrow water recognition in the MNDWI images. This can be accomplished because water pixels have higher value than surrounding pixels in MNDWI images. Our approach is expected to improve the ability of narrow water feature identification by enhancing its spatially implicit characteristics using multi-scale morphological features, e.g., other land cover uses that have similar values in a MNDWI image, such as bare patches and shadows, can be easily identified. Our approach also involves a dual-threshold strategy which is adopted for wide and narrow water body extraction, since a simple threshold is not often an adequate solution [14]. An empirical threshold is used first to obtain possible water areas from a MNDWI image, followed by an automatic threshold which is determined by the maximum interclass variance criterion [15] used for extracting narrow water features from a MNWI image. Finally, a logical operation is performed by combining the two potential water features to identify the true

The remainder of this chapter is organized as follows. In Section 2, we describe the MNWI method of narrow water extraction. Experimental results are shown in Section 3 using multiple experiments on TM images, and we use the MNWI method in a practical application for extracting inland water features in Fujian province,

It is well accepted that open and wide water features can be easily separated from other land cover features by using the NDWI or the MNDWI methods, but extracting narrow water boundaries is generally a more difficult task due to its being confused with built-up areas, roads, hill shadows, etc. Therefore, the goal of our proposed MNWI method is the separation of narrow water and other land cover features by depicting the implicit spectral and structural characteristics of MNDWI. Narrow water usually exhibits strong linear shapes and continuous spatial curves; therefore, we propose a linear enhancement operation on a MNDWI image

**Step 1: Generation of a MNWDI image**. Level 1 T Landsat images in the study region are first collected, which are then corrected geometrically. Atmospheric and radiometric corrections were then applied using the 6S approach to transform the images into reflectance datasets. Because MNWDI performs better in the extraction of water features than NDWI [5], it is selected for initial water extraction and

where Green and MIR are the image reflectance of the green band and medium-

wave infrared band (which correspond to the TM/ETM+ band 5), respectively. **Step 2: Formulation of the MNWI**. MNDWI can improve the local contrast between water and other land cover features, since most water bodies can easily be extracted using a threshold segmentation method. However, narrow water bodies

(*Green* − *MIR*) (*Green* + *MIR*)

(1)

China, in Section 4. Finally, Section 5 presents conclusions.

to form a MNWI image, according to the following steps:

*MNDWI* = \_\_\_\_\_\_\_\_\_\_\_\_

*DOI: http://dx.doi.org/10.5772/intechopen.92311*

water body boundary.

**2. The proposed MNWI method**

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique DOI: http://dx.doi.org/10.5772/intechopen.92311*

denoted as morphological narrow water index (MNWI). The MNWI is constructed using multi-scale and multidirectional differential morphological profiles (DMPs) on a MNDWI image, and then water bodies are automatically extracted using a dual-threshold segmentation. The successful use of DMPs to extract various thematic information from images has been sufficiently validated, such as buildings in urban areas [10, 11], rare earth mining areas [12], and mapping of mangrove forests [13]. In this paper, we introduce a DMP technique to highlight the contrast of bright features as a way of narrow water recognition in the MNDWI images. This can be accomplished because water pixels have higher value than surrounding pixels in MNDWI images. Our approach is expected to improve the ability of narrow water feature identification by enhancing its spatially implicit characteristics using multi-scale morphological features, e.g., other land cover uses that have similar values in a MNDWI image, such as bare patches and shadows, can be easily identified. Our approach also involves a dual-threshold strategy which is adopted for wide and narrow water body extraction, since a simple threshold is not often an adequate solution [14]. An empirical threshold is used first to obtain possible water areas from a MNDWI image, followed by an automatic threshold which is determined by the maximum interclass variance criterion [15] used for extracting narrow water features from a MNWI image. Finally, a logical operation is performed by combining the two potential water features to identify the true water body boundary.

The remainder of this chapter is organized as follows. In Section 2, we describe the MNWI method of narrow water extraction. Experimental results are shown in Section 3 using multiple experiments on TM images, and we use the MNWI method in a practical application for extracting inland water features in Fujian province, China, in Section 4. Finally, Section 5 presents conclusions.

#### **2. The proposed MNWI method**

It is well accepted that open and wide water features can be easily separated from other land cover features by using the NDWI or the MNDWI methods, but extracting narrow water boundaries is generally a more difficult task due to its being confused with built-up areas, roads, hill shadows, etc. Therefore, the goal of our proposed MNWI method is the separation of narrow water and other land cover features by depicting the implicit spectral and structural characteristics of MNDWI. Narrow water usually exhibits strong linear shapes and continuous spatial curves; therefore, we propose a linear enhancement operation on a MNDWI image to form a MNWI image, according to the following steps:

**Step 1: Generation of a MNWDI image**. Level 1 T Landsat images in the study region are first collected, which are then corrected geometrically. Atmospheric and radiometric corrections were then applied using the 6S approach to transform the images into reflectance datasets. Because MNWDI performs better in the extraction of water features than NDWI [5], it is selected for initial water extraction and calculated as:

$$\text{MINDVI} = \frac{(Green - MIR)}{(Green + MIR)} \tag{1}$$

where Green and MIR are the image reflectance of the green band and mediumwave infrared band (which correspond to the TM/ETM+ band 5), respectively.

**Step 2: Formulation of the MNWI**. MNDWI can improve the local contrast between water and other land cover features, since most water bodies can easily be extracted using a threshold segmentation method. However, narrow water bodies

*Inland Waters - Dynamics and Ecology*

to global scales. At a result, it has become a routine approach for the monitoring of land surface water bodies, since the acquired data can provide macroscopic, real-time, dynamic, and cost-effective information, which is substantially different from conventional in situ measurements. Various approaches for water body extraction from multispectral images have been developed in the past decades [2–4], which can be broadly grouped into three categories: spectral band segmentation, image supervised classification, and water indices. Among all these methods, of particular interest is the spectral water index-based method, as it is a reliable and cost-effective method. This type of method takes advantage of reflectivity differences of each involved band for water body extraction based on the analysis of

One of the most widely used indexes is the normalized difference water index (NDWI) [4], which utilizes the green (band 2) and near-infrared (band 4) of Landsat TM to delineate open water features. However, Xu found that the NDWI cannot efficiently suppress the signal from built-up surfaces and therefore proposed an improved one, called modified normalized difference water index (MNDWI) [5], where the NDWI was modified by replacing band 4 with band 5 of Landsat TM/ETM. The MNDWI has been validated as one of the most widely used water indices for various applications, though it is still difficult to obtain a high accuracy of water extraction in complex circumstances. Carleer and Wolff [6], among others, have found that the land cover classifications of water and shadow can often be confused. This issue often arises in environments where a large amount of shadow and water regions exist, such as urban and mountainous landscapes. The identification of narrow water bodies (such as narrow streams, canals, ponds, small reservoirs, etc.) can be a difficult task when using NDWI or MNDWI images, because the shallow and narrow water pixels may generate unstable spectral profiles or characteristics, due to the mixed reflectance caused by sediment and/or adjacent land covers. Narrow water is typically defined as a water body with an apparent width less than or equal to three pixels in an image. Therefore, narrow water features often contain mixed pixels, and the extraction of them from NDWI or MNDWI images generally

To remedy this problem, past studies have attempted to identify narrow water features by combining different procedures. Yang et al. proposed a method of extracting initial water information via a user-defined specified water index, and then they performed a series of operations. These operations include morphological dilation, image filtering, and thinning techniques applied to the water index image to recover the continuity of narrow rivers or streams [7]. This method can be effective in the extraction of narrow water bodies if the water disruption is short; however, it may increase false water identification when water disruption is large, since it is dependent on the morphological dilation operation to reconnect the narrow rivers. Such simple threshold techniques are not often a sufficient solution to identify narrow water bodies; therefore, Li et al. suggested an object-oriented method of small water body extraction [8]. They first extracted textural and shaperelated features from images as supplementary information to spectral bands and then performed a segmentation operation on the images using an optimal scale to identify the potential water bodies. Yet, their method is not an automatic process, since it involves multiple user-defined parameters in image segmentation, which prohibits its use in large areas. An alternative approach was performed by Jiang et al. who extracted narrow water features via the enhancement of linear features in NDWI images [9]. However, their procedure involves multiple empirical thresholds,

so it is not a cost-effective method for water feature extraction on large scale. Attempting to improve on these previous approaches, here we propose an automatic water extraction method that constructs a novel narrow water index,

signature differences between water and other surfaces.

exhibits a discontinuous shape in space.

**140**

#### *Inland Waters - Dynamics and Ecology*

are still difficult to extract, as they are easily confused with urban areas, roads, and mountain shadows because of mixed pixels. To alleviate this problem, we adobe a linear object enhancement technique using a white top-hat transform operation on a MNDWI image via the extraction of multi-scale and multidirectional differential morphological profiles to form a MNWI image, according to the following three sub-procedures:


$$\text{WTH} \{ d, \text{s} \} = \text{MNDWI} - \gamma\_{\text{MNDWI}} \text{(sc)} \tag{2}$$

**143**

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique*

WTH difference is small. With this consideration in mind, we determine the contrast of the maximum and minimum values of the WTH in all directions to

enhance the linear structure further. Thus, the MNWI is formulated as:

*MNWI* = *WTH*Max − *WTH*Min (3)

where WTHMax and WTHMin are the maximum and the minimum values of the

**Step 4**: **Image post-processing**. Small trails might also display a high value in a MNWI image and may be misclassified as a narrow water body. To reduce this error, the difference built-up index (NDBI) [16] can also be used to refine the final result. In the present study, a threshold of NDBI >0.05 is used, so that most of the roads

To evaluate our method, three study regions are taken from two Landsat ETM+/

OLI images with different water body types and different terrains, as shown in **Figure 1**. Study area 1 is a sub-scene image with 1000 by 1000 pixel size chosen from a Landsat 7 ETM+ image acquired on September 1, 2001, centered on the Panjiakou Reservoir near Tangshan and Chengde cities in Hebei province in north-

Study area 2 is also a sub-image of 1000 by 1000 pixels, which is located in Luoyuan County, Fujian province, which is acquired from the Landsat 8 operational Landsat image (OLI) on December 13, 2014. This region contains very narrow streams (**Figure 2b**), and it is used to test the extraction ability from mixed pixels. Study area 3 (**Figure 3c**) is a 1000 by 1000 pixel scene selected from the same OLI image as #2, which is located in southern Youxi County, Fujian province, and covers one of main branches of Minjiang River as well as other narrow streams (Qingyin, Qing, Wenjiang, etc.). Youxi County and several villages are in this study area,

Actual water feature information for these study areas are not available, so the water bodies in the three images are manually digitized using high resolution spatial images to provide a basis map for comparison. High-resolution Google Earth™ images were also used as a complementary reference to assist in distinguishing water pixels that might be confused with background noise, such as mountain shadows, trails and built-up areas.

reconstruction of the white top-hat procedure in all directions, respectively.

to be narrow water; otherwise it is categorized as not water.

and trails are excluded from the final water determinations.

ern China, which covers multiple branches of Luanhe River.

which contain multiple sources of possible background noise.

**3. Method validations**

**Step 3**: **Dual-threshold segmentation**. A simple threshold is not usually adequate to separate water features in large and complex regions from a MNDWI or MNWI image. Therefore, we employ a dual-threshold strategy to delineate water feature characteristics. A relatively large threshold was first determined empirically to separate the MNDWI image into possible water regions, denoted as W1. Experimental results suggest that this threshold should be set at 0.2, such that all wide water bodies were extracted, and most other objects were excluded. However, many narrow water bodies may be missed in this procedure, and small rivers may be of a discontinuous shape in space. Thus, another threshold is determined by the Otsu method [15] performed on the MNWI image to extract possible narrow water bodies, denoted as W2. The final water feature information is then delineated according to the following logical rule: If the possible water in W2 is connected to any wide water extracted from the MNDWI image (i.e., W1), it is then determined

*DOI: http://dx.doi.org/10.5772/intechopen.92311*

where <sup>γ</sup> *MNDWI*(*se*) is the output image yielded by performing a closing operator to a MNDWI image. A closing operator can suppress smaller, darker objects and join adjacent objects together; thus we expect that small water bodies smaller than the structural elements will be highlighted after this reconstruction, and open water bodies and background objects larger than the structural elements should be suppressed. We previously defined a narrow water body as no larger than three pixels; thus, the linear structural elements in our algorithm are extended in four directions (0°, 45°, 90°, and 135°), and each direction was applied with three scales (smin = 1, smax = 3, Δs = 1) to generate the WTH image.

3.**Construction of the morphological narrow water index**. The WTH process essentially suppresses the nonrelevant background, though there still may be small features (e.g., buildings or shadows) that must be removed. Narrow water features have linear features with two main orientations, and the difference between maximum and minimum values of the WTH value in different directions is relatively large. Conversely, the shapes of buildings and mountain shadows usually have polygon-like features, indicating that the *Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique DOI: http://dx.doi.org/10.5772/intechopen.92311*

WTH difference is small. With this consideration in mind, we determine the contrast of the maximum and minimum values of the WTH in all directions to enhance the linear structure further. Thus, the MNWI is formulated as:

$$\text{MINWI} = \text{WTH}\_{\text{Max}} - \text{WTH}\_{\text{Min}} \tag{3}$$

where WTHMax and WTHMin are the maximum and the minimum values of the reconstruction of the white top-hat procedure in all directions, respectively.

**Step 3**: **Dual-threshold segmentation**. A simple threshold is not usually adequate to separate water features in large and complex regions from a MNDWI or MNWI image. Therefore, we employ a dual-threshold strategy to delineate water feature characteristics. A relatively large threshold was first determined empirically to separate the MNDWI image into possible water regions, denoted as W1. Experimental results suggest that this threshold should be set at 0.2, such that all wide water bodies were extracted, and most other objects were excluded. However, many narrow water bodies may be missed in this procedure, and small rivers may be of a discontinuous shape in space. Thus, another threshold is determined by the Otsu method [15] performed on the MNWI image to extract possible narrow water bodies, denoted as W2. The final water feature information is then delineated according to the following logical rule: If the possible water in W2 is connected to any wide water extracted from the MNDWI image (i.e., W1), it is then determined to be narrow water; otherwise it is categorized as not water.

**Step 4**: **Image post-processing**. Small trails might also display a high value in a MNWI image and may be misclassified as a narrow water body. To reduce this error, the difference built-up index (NDBI) [16] can also be used to refine the final result. In the present study, a threshold of NDBI >0.05 is used, so that most of the roads and trails are excluded from the final water determinations.

#### **3. Method validations**

*Inland Waters - Dynamics and Ecology*

sub-procedures:

are still difficult to extract, as they are easily confused with urban areas, roads, and mountain shadows because of mixed pixels. To alleviate this problem, we adobe a linear object enhancement technique using a white top-hat transform operation on a MNDWI image via the extraction of multi-scale and multidirectional differential morphological profiles to form a MNWI image, according to the following three

1.**Define linear structures**. A narrow river or stream has clear linear features with two main directions, but the shapes of buildings and mountain shadows have polygon-like features. Hence, we introduce a DMP method to separate them. The use of DMPs involves the designing of a filtering operator (e.g., size and shape), known as a structural element (SE). This acts as a probe to extract or suppress specific structures by checking that each part of the SE fits within the objects in the image. A single-SE size approach is typically not suitable for complex structures; therefore, a series of linear structural elements are implemented to form DMPs, so that the size and directional bias of the narrow water features are identified clearly. Thus, the linear structure element was defined as se = strelem(*d, s*), where *d* represents the orientation of the linear structure

(e.g., 0°, 45°, 90°, 135°) and *s* denotes the scale of the small water body.

the white-hat MNDWI image is according to:

smax = 3, Δs = 1) to generate the WTH image.

2.**White-hat morphological reconstruction (white top-hat)**. In general, an opening/closing operator can isolate bright or dark structures in an image when the objects are brighter or darker than the surrounding features. An opening operator can help separate water objects from other land cover features since water appears brighter in a MNDWI image. To isolate features that have a thinner support than a given SE, a common practice to use is a top-hat morphological transform in taking the residual of the opening, closing, and original images to ensure a better shape preservation [11–13]. The white tophat reconstruction operation is formulated by subtracting the opening operation from the initial image using the same image. This enhances linear features with a structure smaller than the SE, and a morphological reconstruction of

*WTH*(*d*,*s*) = *MNDWI* − γ*MNDWI*(*se*) (2)

where <sup>γ</sup> *MNDWI*(*se*) is the output image yielded by performing a closing operator to a MNDWI image. A closing operator can suppress smaller, darker objects and join adjacent objects together; thus we expect that small water bodies smaller than the structural elements will be highlighted after this reconstruction, and open water bodies and background objects larger than the structural elements should be suppressed. We previously defined a narrow water body as no larger than three pixels; thus, the linear structural elements in our algorithm are extended in four directions (0°, 45°, 90°, and 135°), and each direction was applied with three scales (smin = 1,

3.**Construction of the morphological narrow water index**. The WTH

process essentially suppresses the nonrelevant background, though there still may be small features (e.g., buildings or shadows) that must be removed. Narrow water features have linear features with two main orientations, and the difference between maximum and minimum values of the WTH value in different directions is relatively large. Conversely, the shapes of buildings and mountain shadows usually have polygon-like features, indicating that the

**142**

To evaluate our method, three study regions are taken from two Landsat ETM+/ OLI images with different water body types and different terrains, as shown in **Figure 1**. Study area 1 is a sub-scene image with 1000 by 1000 pixel size chosen from a Landsat 7 ETM+ image acquired on September 1, 2001, centered on the Panjiakou Reservoir near Tangshan and Chengde cities in Hebei province in northern China, which covers multiple branches of Luanhe River.

Study area 2 is also a sub-image of 1000 by 1000 pixels, which is located in Luoyuan County, Fujian province, which is acquired from the Landsat 8 operational Landsat image (OLI) on December 13, 2014. This region contains very narrow streams (**Figure 2b**), and it is used to test the extraction ability from mixed pixels. Study area 3 (**Figure 3c**) is a 1000 by 1000 pixel scene selected from the same OLI image as #2, which is located in southern Youxi County, Fujian province, and covers one of main branches of Minjiang River as well as other narrow streams (Qingyin, Qing, Wenjiang, etc.). Youxi County and several villages are in this study area, which contain multiple sources of possible background noise.

Actual water feature information for these study areas are not available, so the water bodies in the three images are manually digitized using high resolution spatial images to provide a basis map for comparison. High-resolution Google Earth™ images were also used as a complementary reference to assist in distinguishing water pixels that might be confused with background noise, such as mountain shadows, trails and built-up areas.

**Figure 1.** *The collected images and locations for the study areas.*

**Figure 2.**

*The false-colored images for the three study areas used in our experiments. (a) study area 1, (b) study area 2, (c) study area 3.*

#### **Figure 3.**

*Comparison of small bodies of water in the MNDWI and the MNWI for study area 1 where (a) and (b) are the extracted water bodies with the MNDWI and the MNWI indexes, respectively, and (c) and (d) denote the focused areas highlighted in red boxes.*

**145**

**Figure 4.**

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique*

A comparison between MNDWI and MNWI methods was first described. The two types of water index images for study area 1 are shown in **Figure 3a** and **b**, with focused areas highlighted in red boxes shown in **Figure 3c** and **d**. The pixels' values of water typically have higher values (white areas) than those of the other land cover features in these images, since both the MNDWI and the MNWI water indexes strongly enhance the water body signals. It is also observed in **Figure 3a** and **c** that the brightness difference between wide water and narrow water in the MNDWI image is larger, suggesting that a threshold segmentation on the MNDWI image cannot resolve entire water bodies. In contrast, the difference in the MNWI image is significantly reduced, though they maintain relatively higher values than other land cover features, as shown in **Figure 3b** and **d**. By looking at **Figure 3d**, it is seen that the local contrast between narrow water and other land cover features is significantly enhanced. Additionally, narrow water such as small rivers and branches maintains a continuous spatial shape, suggesting that narrow water features can be accurately extracted with a threshold

Furthermore, 1200 samples of typical land cover types from study area 3 were randomly selected from each category and were analyzed by calculating the maximal value, the minimal value, the mean value, and the deviation. The criteria for the sample selection are the following: (1) Each land cover has ~200 samples to keep a sample balance; and (2) each land cover contains several small patches from different locations to maintain a spectral variety. **Figure 4** reports the spatial distribution of the samples for study area 3 and their statistical information for six typical land cover types, i.e., wide open water, narrow water, vegetation, built-up area, roads, and shadow. As can be seen in **Figure 4**, the values of the wide water are very high for MNDWI. However, it is difficult to discriminate narrow water from other land cover types, especially for shadows, roads, and built-up areas. In contrast, the values of the narrow water in the MNWI method are relatively high compared with

*The spatial distribution of 1200 selected samples for study area 3 (left) and the statistical information of six* 

*typical land cover types for MNDWI and MNWI images, respectively (right).*

*DOI: http://dx.doi.org/10.5772/intechopen.92311*

**3.1 Validation of MNWI features**

implementation.

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique DOI: http://dx.doi.org/10.5772/intechopen.92311*

#### **3.1 Validation of MNWI features**

*Inland Waters - Dynamics and Ecology*

**144**

**Figure 3.**

**Figure 2.**

*(c) study area 3.*

**Figure 1.**

*The collected images and locations for the study areas.*

*focused areas highlighted in red boxes.*

*Comparison of small bodies of water in the MNDWI and the MNWI for study area 1 where (a) and (b) are the extracted water bodies with the MNDWI and the MNWI indexes, respectively, and (c) and (d) denote the* 

*The false-colored images for the three study areas used in our experiments. (a) study area 1, (b) study area 2,* 

A comparison between MNDWI and MNWI methods was first described. The two types of water index images for study area 1 are shown in **Figure 3a** and **b**, with focused areas highlighted in red boxes shown in **Figure 3c** and **d**. The pixels' values of water typically have higher values (white areas) than those of the other land cover features in these images, since both the MNDWI and the MNWI water indexes strongly enhance the water body signals. It is also observed in **Figure 3a** and **c** that the brightness difference between wide water and narrow water in the MNDWI image is larger, suggesting that a threshold segmentation on the MNDWI image cannot resolve entire water bodies. In contrast, the difference in the MNWI image is significantly reduced, though they maintain relatively higher values than other land cover features, as shown in **Figure 3b** and **d**. By looking at **Figure 3d**, it is seen that the local contrast between narrow water and other land cover features is significantly enhanced. Additionally, narrow water such as small rivers and branches maintains a continuous spatial shape, suggesting that narrow water features can be accurately extracted with a threshold implementation.

Furthermore, 1200 samples of typical land cover types from study area 3 were randomly selected from each category and were analyzed by calculating the maximal value, the minimal value, the mean value, and the deviation. The criteria for the sample selection are the following: (1) Each land cover has ~200 samples to keep a sample balance; and (2) each land cover contains several small patches from different locations to maintain a spectral variety. **Figure 4** reports the spatial distribution of the samples for study area 3 and their statistical information for six typical land cover types, i.e., wide open water, narrow water, vegetation, built-up area, roads, and shadow. As can be seen in **Figure 4**, the values of the wide water are very high for MNDWI. However, it is difficult to discriminate narrow water from other land cover types, especially for shadows, roads, and built-up areas. In contrast, the values of the narrow water in the MNWI method are relatively high compared with

#### **Figure 4.**

*The spatial distribution of 1200 selected samples for study area 3 (left) and the statistical information of six typical land cover types for MNDWI and MNWI images, respectively (right).*

other land cover types, indicating that it is relatively easy to separate the narrow water bodies from other land cover types.

It can also be seen in **Figure 5** that the values of objects with polygon-like shapes, such as wide water, built-up areas, and shadows, are heavily suppressed in the MNWI image since they do not exhibit a linear structure. However, roads also show linear structural characteristics; thus they have high values in a MNWI image. This demonstrates that neither MNDWI nor MNWI can effectively identify entire water bodies using a threshold segmentation. To remedy this, we adopted a dual-threshold strategy. The first threshold is used for wide water extraction from MNDWI, and the second is employed to extract narrow water features from MNWI.

#### **3.2 Validation of dual-threshold segmentation**

An empirical threshold (0.2) was first used to perform a rough extraction of potential water features from a MNDWI image; then a second threshold determined by Otsu was determined from the MNWI image for possible narrow water features. Next, a combing procedure was carried out to extract entire water bodies using an "if-then" logic calculation according to the following rule: If two potential water regions are spatially connected, then they are determined to be water bodies; otherwise they are determined to be other land cover types.

As a demonstration of the dual-threshold segmentation method, comparisons between single threshold segmentation of a MNDWI image and dual-threshold segmentation of a MNWI image are shown in **Figure 6(a)**–**(c)**. It is seen that when a smaller threshold (T = 20) is adopted, a narrow stream keeps a relatively complete spatial shape, yet it also contains a trail (road) at the bottom of the image (**Figure 6a**). However, if we increase the threshold T to 40, this trail is no longer extracted, but the stream exhibits discontinuities along the stream. Thus, the use of a dual-threshold segmentation can better identify this stream as continuous and avoid the identification of the trail.

#### **3.3 Visual assessment**

**Figure 7** presents the extracted water features using our proposed method for each of the three study areas. As a comparison, water information derived from the MNDWI image using an optimal threshold segmentation is also listed. For clarity, the corrected, misclassified, and omitted water information is labeled with different color schemes. Visual inspection shows that our method significantly outperforms the MNDWI method when using an optimal threshold segmentation. It can be seen that the majority of narrow rivers in each of the study areas are successfully extracted by our method. Six branches of the Luanhe River are

#### **Figure 5.**

*Illustration of the linear enhancement and polygon compression of different land cover types in study area 3, where (a) and (c) are the MNDWI and the MNWI features, respectively, and (b) and (d) are the corresponding focused areas.*

**147**

**Figure 7.**

as most of them are ignored.

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique*

*Segmentation performed on the focused region of study area 1 using different thresholds, where (a), (b), and (c) are obtained by a threshold T equal to 20, 30, and 40, respectively, and (d) is the same image using a* 

clearly delineated in study area 1, and most narrow streams in study areas 2 and 3 are clearly extracted. However, a few narrow tributaries were misclassified by the MNDWI method, highlighted in red in **Figure 7**. A closer inspection of study area 2 shows that there are still two omissions which are highlighted with white rectangles, due to the width of two streams being too narrow (less than 10 m) to occupy a footprint, and the reflectance of these pixels are strongly mixed with other land cover types. Conversely, the results derived from the MNDWI image are less effective, as only small portions of the narrow rivers were extracted correctly. This is especially true for the narrow streams in the top region of the image,

*our method and the optimal threshold segmentation method, respectively.*

*Water extraction results from the three study areas, where the first and second lines are the results extracted by* 

Another misclassification issue is the delineation of the sides of rivers, due to mixed pixel effects. Another experiment in the study area 3 was conducted to demonstrate this. These results are reported in **Figure 8**, where the water information that was corrected, omitted, and misclassified is shown in cyan, magenta, and red, respectively. It can be found that the boundary of the Youxi River can be accurately

*DOI: http://dx.doi.org/10.5772/intechopen.92311*

**Figure 6.**

*dual-threshold segmentation.*

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique DOI: http://dx.doi.org/10.5772/intechopen.92311*

#### **Figure 6.**

*Inland Waters - Dynamics and Ecology*

water bodies from other land cover types.

**3.2 Validation of dual-threshold segmentation**

avoid the identification of the trail.

**3.3 Visual assessment**

otherwise they are determined to be other land cover types.

other land cover types, indicating that it is relatively easy to separate the narrow

It can also be seen in **Figure 5** that the values of objects with polygon-like shapes, such as wide water, built-up areas, and shadows, are heavily suppressed in the MNWI image since they do not exhibit a linear structure. However, roads also show linear structural characteristics; thus they have high values in a MNWI image.

This demonstrates that neither MNDWI nor MNWI can effectively identify entire water bodies using a threshold segmentation. To remedy this, we adopted a dual-threshold strategy. The first threshold is used for wide water extraction from MNDWI, and the second is employed to extract narrow water features from MNWI.

An empirical threshold (0.2) was first used to perform a rough extraction of potential water features from a MNDWI image; then a second threshold determined by Otsu was determined from the MNWI image for possible narrow water features. Next, a combing procedure was carried out to extract entire water bodies using an "if-then" logic calculation according to the following rule: If two potential water regions are spatially connected, then they are determined to be water bodies;

As a demonstration of the dual-threshold segmentation method, comparisons between single threshold segmentation of a MNDWI image and dual-threshold segmentation of a MNWI image are shown in **Figure 6(a)**–**(c)**. It is seen that when a smaller threshold (T = 20) is adopted, a narrow stream keeps a relatively complete spatial shape, yet it also contains a trail (road) at the bottom of the image (**Figure 6a**). However, if we increase the threshold T to 40, this trail is no longer extracted, but the stream exhibits discontinuities along the stream. Thus, the use of a dual-threshold segmentation can better identify this stream as continuous and

**Figure 7** presents the extracted water features using our proposed method for each of the three study areas. As a comparison, water information derived from the MNDWI image using an optimal threshold segmentation is also listed. For clarity, the corrected, misclassified, and omitted water information is labeled with different color schemes. Visual inspection shows that our method significantly outperforms the MNDWI method when using an optimal threshold segmentation. It can be seen that the majority of narrow rivers in each of the study areas are successfully extracted by our method. Six branches of the Luanhe River are

*Illustration of the linear enhancement and polygon compression of different land cover types in study area 3, where (a) and (c) are the MNDWI and the MNWI features, respectively, and (b) and (d) are the* 

**146**

**Figure 5.**

*corresponding focused areas.*

*Segmentation performed on the focused region of study area 1 using different thresholds, where (a), (b), and (c) are obtained by a threshold T equal to 20, 30, and 40, respectively, and (d) is the same image using a dual-threshold segmentation.*

#### **Figure 7.**

*Water extraction results from the three study areas, where the first and second lines are the results extracted by our method and the optimal threshold segmentation method, respectively.*

clearly delineated in study area 1, and most narrow streams in study areas 2 and 3 are clearly extracted. However, a few narrow tributaries were misclassified by the MNDWI method, highlighted in red in **Figure 7**. A closer inspection of study area 2 shows that there are still two omissions which are highlighted with white rectangles, due to the width of two streams being too narrow (less than 10 m) to occupy a footprint, and the reflectance of these pixels are strongly mixed with other land cover types. Conversely, the results derived from the MNDWI image are less effective, as only small portions of the narrow rivers were extracted correctly. This is especially true for the narrow streams in the top region of the image, as most of them are ignored.

Another misclassification issue is the delineation of the sides of rivers, due to mixed pixel effects. Another experiment in the study area 3 was conducted to demonstrate this. These results are reported in **Figure 8**, where the water information that was corrected, omitted, and misclassified is shown in cyan, magenta, and red, respectively. It can be found that the boundary of the Youxi River can be accurately

**Figure 8.**

*The results of the river side misclassification experiment performed on study area 3. (a) the original image, (b) and (c) are the extracted water features in the focused area using out-proposed and the OT method, respectively.*

extracted with the proposed method as shown in **Figure 8b**. However, using the MNDWI method with an optimal threshold, the omitted water pixels were along both sides of the river boundary (**Figure 8c**).

#### **3.4 Quantitative evaluation**

We now quantitatively evaluate our extracted results. Four measurements are used for comparison; the user and producer accuracy, the kappa coefficient, and the overall accuracy. Additionally, two recently developed methods for narrow water extraction, i.e., the method developed by Yang et al. [7] and the linear feature enhancement (LFE) developed by Jiang et al. [9], are also included for comparison. **Table 1** gives a pixel-by-pixel analysis of the classification accuracies for all datasets, with the best results highlighted in bold.

It can be seen in **Table 1** that the optimal threshold segmentation method was the least accurate, as it failed nearly completely in study area 2 with a 35% product accuracy and a kappa coefficient of 0.477. The method of Yang has some similar effects in narrow water extraction to our datasets, especially for mixed water features. The method of Jiang significantly improves the accuracy of narrow water extraction as compared to the optimal threshold segmentation method, as most of the narrow streams are well extracted in each of the study areas and had a comparable accuracy to our method. However, it should also be noted that this method is not an automatic method, since many parameters need to be tuned, which prevents it from being effectively used in larger areas. Overall, our method outperforms all others in terms of measurements except for producer accuracy in study area 3, where Yang's method achieves a relatively higher accuracy.

**149**

**Table 2.**

Acquisition time

Acquisition time

**Table 1.**

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique*

**Methods Optimal threshold Yang Jiang Ours** Study area 1 Producer accuracy 53.8% 75.1% 92.1% **92.3%**

Study area 2 Producer accuracy 35.2% 43.6% 82.8% **83.9%**

Study area 3 User accuracy 87.9% 73.8% 96.6% **98.9%**

User accuracy 79.8% 85.3% 92.8% **95.6%** Overall accuracy 67.3% 79.5% 91.3% **93.6%** Kappa 0.631 0.748 0.907 **0.924**

User accuracy 83.9% 57.6% 99.1% **99.6%** Overall accuracy 55.4% 48.5% 89.2% **90.7%** Kappa 0.477 0.453 0.872 **0.885** Producer accuracy 56.3% 55.5% **87.1%** 86.9%

Overall accuracy 71.2% 65.8% 90.3% **91.6%** Kappa 0.696 0.627 0.881 **0.905**

*DOI: http://dx.doi.org/10.5772/intechopen.92311*

**4. Extraction of inland water of Fujian province**

relatively good, with cloud cover less than 10%.

December 3

December 1

*The information of collected Landsat 8 OLI images covering Fujian province in 2013.*

November 17

December 1

is a relatively large region that covers an area of about 121,000 km2

The aforementioned experiments demonstrate that the MNWI is the most efficient algorithm for narrow water extraction, but it is still interest to address whether it is applicable to large-volume data in an actual scenario. Therefore, we apply our method to extract inland water features in Fujian province, China, which

*Comparison of accuracies for different water extraction methods, with the best results given in bold text.*

mountainous province, located on the southeast coast of China and facing Taiwan across the Taiwan Strait. It has significant vegetation cover because of high mean precipitation and warm annual temperatures. Topographically, Fujian is a very mountainous region, having abundant water resources, rivers, lakes, and reservoirs. Many rivers run through these mountains, of which the most important is the Min River, as its drainage area covers over 50% of the province. The upstream Jin River, Futun River, and Shaowu River all converge into the Min River. The Jiulong River flows south of the Min River, reaching the sea at Xiamen city, and the Ting River runs across Fujian's southwestern border. It is thus an appropriate region to test our methods in a large area. To cover the entirety of Fujian province, 13 Landsat 8 OLI images were collected. Fujian is usually cloudy and rainy in spring and summer, so we collected all the images in winter to avoid cloud interference. The acquisition information is summarized in **Table 2**. Note that the quality of all acquired data is

Path/row 118/041 118/042 119/041 119/042 119/043 120/040 120/041

October 23

October 5

October 23

October 5

December 1

October 5

December 1

October 23

December 1

Path/row 120/042 120/043 120/044 121/041 121/042 121/043

. Fujian is a


*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique DOI: http://dx.doi.org/10.5772/intechopen.92311*

**Table 1.**

*Inland Waters - Dynamics and Ecology*

extracted with the proposed method as shown in **Figure 8b**. However, using the MNDWI method with an optimal threshold, the omitted water pixels were along

*The results of the river side misclassification experiment performed on study area 3. (a) the original image, (b) and (c) are the extracted water features in the focused area using out-proposed and the OT method,* 

We now quantitatively evaluate our extracted results. Four measurements are used for comparison; the user and producer accuracy, the kappa coefficient, and the overall accuracy. Additionally, two recently developed methods for narrow water extraction, i.e., the method developed by Yang et al. [7] and the linear feature enhancement (LFE) developed by Jiang et al. [9], are also included for comparison. **Table 1** gives a pixel-by-pixel analysis of the classification accuracies for all datasets,

It can be seen in **Table 1** that the optimal threshold segmentation method was the least accurate, as it failed nearly completely in study area 2 with a 35% product accuracy and a kappa coefficient of 0.477. The method of Yang has some similar effects in narrow water extraction to our datasets, especially for mixed water features. The method of Jiang significantly improves the accuracy of narrow water extraction as compared to the optimal threshold segmentation method, as most of the narrow streams are well extracted in each of the study areas and had a comparable accuracy to our method. However, it should also be noted that this method is not an automatic method, since many parameters need to be tuned, which prevents it from being effectively used in larger areas. Overall, our method outperforms all others in terms of measurements except for producer accuracy in study area 3, where Yang's method achieves a relatively

both sides of the river boundary (**Figure 8c**).

with the best results highlighted in bold.

**3.4 Quantitative evaluation**

**Figure 8.**

*respectively.*

**148**

higher accuracy.

*Comparison of accuracies for different water extraction methods, with the best results given in bold text.*

#### **4. Extraction of inland water of Fujian province**

The aforementioned experiments demonstrate that the MNWI is the most efficient algorithm for narrow water extraction, but it is still interest to address whether it is applicable to large-volume data in an actual scenario. Therefore, we apply our method to extract inland water features in Fujian province, China, which is a relatively large region that covers an area of about 121,000 km2 . Fujian is a mountainous province, located on the southeast coast of China and facing Taiwan across the Taiwan Strait. It has significant vegetation cover because of high mean precipitation and warm annual temperatures. Topographically, Fujian is a very mountainous region, having abundant water resources, rivers, lakes, and reservoirs. Many rivers run through these mountains, of which the most important is the Min River, as its drainage area covers over 50% of the province. The upstream Jin River, Futun River, and Shaowu River all converge into the Min River. The Jiulong River flows south of the Min River, reaching the sea at Xiamen city, and the Ting River runs across Fujian's southwestern border. It is thus an appropriate region to test our methods in a large area. To cover the entirety of Fujian province, 13 Landsat 8 OLI images were collected. Fujian is usually cloudy and rainy in spring and summer, so we collected all the images in winter to avoid cloud interference. The acquisition information is summarized in **Table 2**. Note that the quality of all acquired data is relatively good, with cloud cover less than 10%.


**Table 2.**

*The information of collected Landsat 8 OLI images covering Fujian province in 2013.*

**Figure 9.** *The mosaic image and the final result of inland water bodies in Fujian province, China.*

All the images were matched and stitched without altering their spectral color (**Figure 9**, left), and the final inland water information for the Fujian province (**Figure 9**, right) shows that 2,494,988 pixels were classified into inland surface water. It can be calculated that the total inland water area of Fujian province is about 2245.49 km<sup>2</sup> in the winter of 2013. Visually, our method can extract the most of perceptible water bodies with a high accuracy, where the main rivers, such as Min River, Jiurong River, Ting River, etc., are all correctly delineated with clear river boundaries. Moreover, most of the spatial shapes of small tributaries were continuous and so were the lakes and reservoirs. To evaluate the quantitative classification accuracy, 6800 samples of water and non-water features were randomly selected. The water samples included 3340 pixels, of which wide water to narrow water ratio was about 2:1, as the non-water samples were 3460 pixels, chosen from possibly confused land cover types such as forest, built-up areas, and rare soil. The producer accuracy, user accuracy, overall accuracy, and kappa coefficient calculated from these samples are 94.33%, 98.7%, 96.61%, and 0.932, respectively, indicating that the proposed method can achieve a high accuracy for water extraction in a large and complex area and it is an effective optional tool for practical water extraction.

#### **5. Conclusions**

Most water indices can perform well for the extraction of wide water features from remote sensing images, but they are normally ineffective in the extraction of narrow water features. This chapter has described a new method using a morphological top-hat transform to form a novel narrow water index, denoted as MNWI, which improves the extraction accuracy of narrow water from Landsat images. Experimental results demonstrated impressive performances of our method of the narrow water extraction. A case study in Fujian province suggests that it is an effective and practical tool for large area inland water.

**151**

**Author details**

\*, Zhang Jinmu<sup>2</sup>

Technology, Xuzhou, China

and Zhao Yindi3

Education, Jiangxi Normal University, Nanchang, China

\*Address all correspondence to: mywubo@fzu.edu.cn

provided the original work is properly cited.

1 School of Geography and Environment, Jiangxi Normal University, Nanchang,

2 Key Laboratory of Poyang Lake Wetland and Watershed Research, Ministry of

3 School of Environment and Spatial Informatics, China University of Mining and

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Wu Bo1

China

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique*

Funding was provided by the Natural Science Foundation of China (Grant No.

*DOI: http://dx.doi.org/10.5772/intechopen.92311*

**Acknowledgements**

41571330, 41830108).

*Improved Narrow Water Extraction Using a Morphological Linear Enhancement Technique DOI: http://dx.doi.org/10.5772/intechopen.92311*

### **Acknowledgements**

*Inland Waters - Dynamics and Ecology*

about 2245.49 km<sup>2</sup>

**Figure 9.**

water extraction.

**5. Conclusions**

All the images were matched and stitched without altering their spectral color (**Figure 9**, left), and the final inland water information for the Fujian province (**Figure 9**, right) shows that 2,494,988 pixels were classified into inland surface water. It can be calculated that the total inland water area of Fujian province is

*The mosaic image and the final result of inland water bodies in Fujian province, China.*

of perceptible water bodies with a high accuracy, where the main rivers, such as Min River, Jiurong River, Ting River, etc., are all correctly delineated with clear river boundaries. Moreover, most of the spatial shapes of small tributaries were continuous and so were the lakes and reservoirs. To evaluate the quantitative classification accuracy, 6800 samples of water and non-water features were randomly selected. The water samples included 3340 pixels, of which wide water to narrow water ratio was about 2:1, as the non-water samples were 3460 pixels, chosen from possibly confused land cover types such as forest, built-up areas, and rare soil. The producer accuracy, user accuracy, overall accuracy, and kappa coefficient calculated from these samples are 94.33%, 98.7%, 96.61%, and 0.932, respectively, indicating that the proposed method can achieve a high accuracy for water extraction in a large and complex area and it is an effective optional tool for practical

Most water indices can perform well for the extraction of wide water features from remote sensing images, but they are normally ineffective in the extraction of narrow water features. This chapter has described a new method using a morphological top-hat transform to form a novel narrow water index, denoted as MNWI, which improves the extraction accuracy of narrow water from Landsat images. Experimental results demonstrated impressive performances of our method of the narrow water extraction. A case study in Fujian province suggests that it is an effective and practical tool for large area inland

in the winter of 2013. Visually, our method can extract the most

**150**

water.

Funding was provided by the Natural Science Foundation of China (Grant No. 41571330, 41830108).

### **Author details**

Wu Bo1 \*, Zhang Jinmu<sup>2</sup> and Zhao Yindi3

1 School of Geography and Environment, Jiangxi Normal University, Nanchang, China

2 Key Laboratory of Poyang Lake Wetland and Watershed Research, Ministry of Education, Jiangxi Normal University, Nanchang, China

3 School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou, China

\*Address all correspondence to: mywubo@fzu.edu.cn

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **References**

[1] Sun F, Sun W, Chen J, Gong P. Comparison and improvement of methods for identifying water bodies in remotely sensed imagery. International Journal of Remote Sensing. 2012;**33**:6854-6875

[2] Frazier PS, Page KJ. Water body detection and delineation with Landsat TM data. Photogrammetric Engineering and Remote Sensing. 2000;**66**:1461-1468

[3] Rokni K, Ahmad A, Solaimani K, Hazini S. A new approach for surface water change detection: Integration of pixel level image fusion and image classification techniques. International Journal of Applied Earth Observation and Geoinformation. 2015;**34**:226-234

[4] McFeeters S. The use of the normalized difference water index (NDWI) in the delineation of open water features. International Journal of Remote Sensing. 1996;**17**:1425-1432

[5] Xu H. Modification of normalised difference water index (NDWI) to enhance open water features in remotely sensed imagery. International Journal of Remote Sensing. 2006;**27**:3025-3033

[6] Carleer AP, Wolff E. Urban land cover multi-level region-based classification of VHR data by selecting relevant features. International Journal of Remote Sensing. 2006;**27**(6):1035-1051

[7] Yang S, Xue S, Liu T. Method for automatically extracting fine water body by using TM image. Journal of Surveying and Mapping (in Chinese with English Abstract). 2010;**39**(6):611-617

[8] Li Y, Ding J, Yan R. Study on extraction method of small water bodies in mountainous area based on GF-1 remote sensing images. Resource Science (in Chinese with English Abstract). 2015;**37**(2):408-416

[9] Jiang H, Feng M, Zhu Y. An automated method for extracting rivers and lakes from Landsat imagery. Remote Sensing. 2014;**6**(6):5067-5089

[10] Beneditsson JA, Pesaresi M, Arnason K. Classification and feature extraction for remote sensing images from urban area based on morphological transformations. IEEE Transaction on Geosciences and Remote Sensing. 2003;**41**(9):1940-1949

[11] Huang X, Zhang L. A multidirectional and multi-scale morphological index for automatic building extraction from multispectral GeoEye-1 imagery. Photogrammetric Engineering & Remote Sensing. 2011;**77**(7):721-732

[12] Wu B, Fang C, Yu L, Huang X, Zhang Q. A fully automatic method to extract rare earth mining area from Landsat image. Photogrammetric Engineering and Remote Sensing. 2016;**82**(9):55-64

Section 4

Biodiversity of Inland Waters

**153**

[13] Huang X, Zhang L, Wang L. Evaluation of morphological texture features for mangrove forest mapping and species discrimination using multispectral IKONOS imagery. IEEE Geoscience and Remote Sensing Letters. 2009;**6**(3):393-397

[14] Ji L, Zhang L, Wylie B. Analysis of dynamic thresholds for the normalized difference water index. Photogrammetric Engineering and Remote Sensing. 2009;**75**(11):1307-1317

[15] Otsu N. A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man and Cybernetics. 1979;**9**(1):62-66

[16] Zha Y, Gao Y, Ni S. Use of normalized difference built-up index in automatically mapping urban areas from TM imagery. International Journal of Remote Sensing. 2003;**24**(3):583-594

Section 4
